Undies Emojis & Symbols

⠀⠀⠀⣠⣤⣤⠄⢤⣤⣤⣤⣤⣤⡀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣀⣀⣀⣀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣀
⠀⠀⠀⣿⣿⣿⣿⡆⠃⡑⣟⣿⣿⣷⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⠙⢿⣯⠉⠉⠉⢉⣿⠟⠛⠃⠀⠀⠀⢀⠀⢠⠀⠀⠀⠀⠈
⠀⠀⠀⠻⠿⣯⠩⠀⠀⠃⠚⣿⠟⠋⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠑⡄⣾⢷⠎⠀⠀⠀⠀⠀⠀⠀⠉⠒⠹⢿⣿⣿⣿⠟⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⢹⡇⢸⡏⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠘⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠾⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠄⠀⠀⠠⠀⠀⠁

⠀⠀⠀⠀⣠⣀⣀⣀⣠⣀⣀⣠⣤⠀⠀⠀⠀⢀⣄⣀⣀⣀⣄⣤⣀⣀⣀⣠⡀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⢀⣀⣀⣀⣀⣄⣀⣀⣀
⠀⠀⠀⠨⠀⠀⠀⠀⠉⠀⠀⠠⠀⠀⠀⠀⠀⢸⣀⣔⠍⠍⡛⢏⣟⢘⢮⡳⡇⠀⠀⠈⠁⠉⠫⡉⢝⢻⣿⡟⢩⠟⠉⠉⠀⠀⠙⠫⠿⠙⢉⠛⣉⠋⠙⠛⣻⠇
⠀⠀⠀⠶⠞⠀⠀⠀⠀⠀⠀⠀⠱⠒⠀⠀⠀⠸⠬⢷⣆⠞⢇⠀⠾⠠⣦⠥⠇⠀⠀⠀⠀⠀⠀⠈⠧⠋⠙⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣅⣎⣤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡾
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⢀⣤⣤⣄⣄⣀⣀⣀⣀⣀⣀⣀
⠀⠀⢰⡟⢳⣲⣶⢾⣷⣶⣶⣶⣶⣶⠀⠀⠀⠀⣿⣦⡀⣀⠀⠀⠀⠀⣀⡴⢻⡧⠀⠀⠀⠀⠈⢻⣇⠀⠀⠀⣹⠟⠉⠉⠀⠀⠀⠛⠒⠭⠉⢍⣹⣉⠉⠡⠐⠋
⠀⠀⠙⠛⢉⣿⣿⣂⠐⡋⢯⣟⠛⠛⠁⠀⠀⢐⢿⡮⣱⣤⣺⣷⣾⣯⢞⣤⣻⠏⠀⠀⠀⠀⠀⠀⠹⡆⠀⢰⡏⠀⠀⠀⠀⠀⠀⠒⠶⢐⢀⣾⣿⣿⣆⢀⠠
⠀⠀⠀⠀⠀⠘⢿⣥⣥⣭⡟⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⣸⣿⣿⣿⣿⣥⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠈⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡴⠦⠤⠤⢤⣄⣀⣀⣀⢀⡤⠤⠤⠴⢶⡀
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡘⠙⠒⠒⠢⠤⠤⠤⠤⠤⠤⠤⠴⠒⠒⠋⢣
⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⢠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠹⣖⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢖⠟⠁
⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠈⠳⢝⢦⠀⠀⠀⠀⠀⠀⠀⡠⣪⠔⠁
⠀⠀⠈⠙⠡⢄⡀⠄⡀⠀⢀⠄⠀⠠⠀⠀⠀⠀⢀⡀⠤⠛⠉⠀⠀⠀⠀⠀⠀⠀⠑⢷⣄⣀⣀⣀⣀⡾⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠘⠓⠂⠀⠀⠀⠈⠒⠓⠈⠁
⠀⠀⠀⠀⠀⠀⠤⠤⠄⠀⢀⣀⣀⣀⡀⠀⠠⠤⠤⡀
⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠸⠯⠭⠭⠿⢷⣖⣒⣒⣒⣲⣾⠿⠯⠭⠭⢷
⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠘⢏⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⡩⠋
⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠑⢄⠱⡄⠀⠀⠀⠀⠀⢀⠞⣡⠞
⠀⠀⠘⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠓⠀⠀⠀⠀⠀⠀⠈⠳⣜⡄⠀⠀⠀⢠⢋⠔⠁
⠀⠀⠀⠀⠀⠉⠐⠊⠔⢤⠀⠁⠀⠀⠑⣤⠄⠄⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠤⠀⠚⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣭⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣽⣽⣽⣿⣯⣭⣽

⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⣰⣿⡿⣿⣷⣄⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⣠⣾⣿⢿⣿⣆
⢠⣿⡟⠀⠀⠻⢿⣿⣿⠿⢿⣿⣦⡀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⢀⣴⣿⡿⠿⣿⣿⡿⠟⠀⠀⣿⣿
⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠿⠿⣿⣶⣤⣴⣶⣶⣦⡀⠀⣀⣠⣄⣀⠀⢀⣴⣶⣶⣦⣤⣶⣿⠿⠿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿
⢸⣿⣧⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠙⠻⣿⣿⣿⠿⠿⣿⣿⣿⠟⠋⠉⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣼⣿
⢸⣿⡿⠛⠻⣿⣷⣄⣤⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⣠⣾⣿⠟⠛⢿⣿
⢸⣿⡇⠀⠀⠈⠛⠛⠛⠋⠙⢿⣿⣤⣠⣴⣶⣶⣶⣿⡿⠛⠛⢿⣿⣶⣤⣀⠀⠀⣀⣤⣶⣿⡿⠛⠛⢿⣿⣶⣶⣶⣦⣄⣤⣿⡿⠋⠙⠛⠟⠛⠁⠀⠀⢸⣿
⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠛⠉⢹⣿⣟⠀⠀⠀⠀⠈⠙⣻⣿⣿⣿⣿⣟⠋⠁⠀⠀⠀⠀⣻⣿⡋⠉⠛⠻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣸⣿⠃⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣀⣠⣤⣶⣿⣿⣿⠟⢻⣿⣿⣿⣶⣤⣄⣀⣴⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⢸⣿
⣿⣿⠀⠀⢿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠛⠋⣽⣿⠏⠀⠀⠹⣿⣧⠙⠛⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⡿⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣶⣶⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⡀⠀⠀⠸⣿⡿⠃⠀⠀⠀⣾⣿⠃⠀⠀⠀⠀⠘⣿⣷⠀⠀⠀⠘⢿⣿⠇⠀⠀⢀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣿
⠙⢿⣿⣯⡀⠀⠀⠀⠀⠈⠉⠙⠛⠿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠿⠛⠋⠉⠁⠀⠀⠀⠀⢀⣽⣿⡿
⠀⠀⠉⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠉
⠀⠀⠀⠀⠈⠛⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣷⡄⠀⠀⣼⣿⣷⠀⠀⠀⠀⣾⣿⣧⠀⠀⢠⣾⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣆⠀⠈⠙⠁⠀⠀⠀⠀⠈⠋⠁⠀⣰⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣄⠀⠀⠀⠘⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⠃⠀⠀⠀⣠⣾⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣦⡀⠀⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⠀⢀⣴⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣦⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣴⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⣶⠶⠾⠿⠿⠿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⡿⠿⠿⢶⡆
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢠⠟⠉⠛⠛⠛⠛⠛⠛⠒⠒⠒⢲⡖⢲⠖⠒⠒⠒⠒⠒⠒⢶⠲⡶⠒⠒⠒⠒⠚⠛⠛⠛⠛⠛⠙⢧
⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⡟⠀⠀⠀⠀⠀⠀⠀⠸⡆⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⢠⠿⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⡈⣧⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠞⣧
⠀⠀⢻⡷⣶⣬⣙⠳⢦⣀⠀⠀⠀⠀⢀⡟⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠸⣇⠀⠀⠀⠀⣠⡴⠛⢉⣠⣴⡶⣿⠃
⠀⠀⠀⠹⣌⢷⡈⠛⢦⣉⠳⢦⡀⠀⡾⢁⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢹⡄⠀⣠⠞⢁⣠⠞⠋⣱⠏⣼⠃
⠀⠀⠀⠀⠙⢧⡙⣦⡀⠉⠳⣄⠙⠾⠃⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠻⠞⢁⣴⠟⠁⢀⡼⢃⡾⠁
⠀⠀⠀⠀⠀⠈⠻⣌⠳⣄⠀⠈⢳⣄⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⣰⠟⠁⠀⣰⠏⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠳⣄⠀⠙⢦⡈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⢀⡼⠃⠀⣠⠞⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣬⡻⢦⡈⢳⡄⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢠⡞⢁⣴⢞⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣝⠳⣿⡄⠹⡆⠀⠀⠀⠀⠀⠀⢠⡏⢠⣿⠶⣋⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣽⡄⢻⡀⠀⠀⠀⠀⠀⡾⢠⣿⡵⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠒⠒⠒⠒⠛⠛⠋⠁

⠀⠀⠀⠀⠀⣠⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⣼⠁⠀⠒⠠⠤⠤⠤⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠉⠉⠉⠉⠉⠛⠻⠶⢦⡀
⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⣇⠀⣀⠴⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⢠⡀⢸⡇
⠀⠀⠀⠈⠛⣿⠀⠀⠁⠒⠀⠁⠁⢄⣀⠠⠒⠄⣀⡠⠊⠂⠀⠀⠈⠑⠄⠀⠂⠉⠒⠄⠐⠉⠒⠀⠀⠁⢸⡏
⠀⠀⠀⠀⠀⢻⠆⠀⠀⢠⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠈⠙⠲⠦⣄⣀⠀⠀⢡⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠉⠁⢈⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡬⠀⢀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠐⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡆⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡱⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋





⣿⣿⣿⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣟⣛

⠀⠀⢠⡶⠶⠦⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⡤⠴⠶⣶
⠀⠀⢸⣧⣄⣀⣀⣀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⢀⣀⣀⣀⣤⣿
⠀⠀⢸⡇⠀⠉⠉⠉⠛⠛⠛⠛⠒⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠚⠛⠛⠛⠋⠉⠉⠁⠀⣿
⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢻⣟⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠞⣻⠟
⠀⠀⠀⠀⠹⣦⠀⠈⠙⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠁⢀⡾⠃
⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠉⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠀⠀⠀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠈⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⡀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⢸⡇⠀⠀⠀⠀⠀⠀⢸⠃⣠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⠶⠴⠤⠤⠤⠤⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣶⣿⣿⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⠐⠁⠀⣰⣿⣿⣿⣿⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⣿⣀⠟⠿⠟⢻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠛⠄⢀⡀⠀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠁⠰⠆⠈⠡⠁⠀⠐⠄⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢀⣈⠤⢀⢤⣾⣀⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠒⠉⠀⠀⠀⠈⠙⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⡀⠀⠘⠁⠀⠀⠀⠀⠀⠀⡀⠀⠉⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⡀⠰⠀⠀⠀⠀⠀⠈⠀⠤⠄⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠶⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠈⠀⠀⢀⠀⢤⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠛⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡿⠋⡻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠙⢿⣿⡧⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡄⠀⠀⠀⠀⠀⠀⢰⣦⣤⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⢰⣾⣷⣶⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠎⠀⠀⠀⠀⠀⠈⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⡀⣠⣤⣤⡶⣗⣲⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣿⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣦⠀⡀⠀⠀⠁⠀⠀⣱⣿⣾⣿⣿⣥⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣡⠇
⠀⠀⠀⠀⠀⠀⠀⠁⠈⠑⠀⠀⠀⠀⠐⣿⣿⡷⢿⣿⣷⡆⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣋⣘
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⢀⠀⠀⠈⠻⣿⣞⣿⣟⣽⡏⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⡠⡜⠐⠀⠀⠀⠀⠈⠈⠛⠷⣅⣈⣧⡀⠀⠀⠀⠀⠀⠀⢠⡟⣿⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢚⠟⠀⠀⠐⠄⠁⠠⢄⡀⠀⠀⠈⠙⠣⢿⣄⠀⠈⣼⡿⣿⢛⡻⢿⣇⣻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⢤⣀⡉⠂⣼⣿⣵⣯⣾⡱⣔⢌⢹⣟⣶⢶⣒⣲⣒⡶⢒⣲⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢹⣿⣆⠀⠓⡵⣾⣽⡿⣦⣧⣻⣽⡏⠝⢯⣹⣛⣿⡿⡿⣿⣿⣷⣤⣄⣄⣤⡴
⢚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣙⣶⣤⣤⣿⣿⣿⣦⣠⣿⣿⣿⣿⣯⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣧⣿⡏
⠀⠀⠀⠉⣴⣶⣦⣤⣤⣀⣀⡈⠀⠀⠲⠈⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄

⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⠤⠶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠦⠤⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⢸⡏⠓⠒⠒⠒⠶⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠖⠒⠒⠒⠋⣿
⠀⠀⠀⠀⠀⠀⢸⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿
⠀⠀⠀⠀⠀⢀⡎⠀⠈⠉⠉⠉⠉⠉⢙⣿⠞⠓⠒⠒⠒⠒⠛⢿⢟⠉⠉⠉⠉⠉⠉⠀⠈⣆
⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀
⠀⠀⣰⢧⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⡎⡇⠀⠀⠀⠀⠀⠀⡏⡞⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣳⡀
⠀⠀⢯⡉⠓⠒⠺⠭⢗⣲⠤⣄⡀⠀⠀⠹⡜⣄⣠⠤⢤⣀⡜⡼⠁⠀⢀⣀⣤⣴⡶⠿⠛⠛⠋⠉⣉⠇
⠀⠀⠀⠉⠲⢤⣀⠀⠀⠀⠉⠓⠻⢷⣦⣄⣘⠞⠀⠀⠀⠘⢞⣀⣤⡾⠟⠛⠉⠀⠀⠀⢀⣠⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⢤⣄⣈⣹⠏⠀⠀⠀⠀⠀⠈⢿⣁⣀⣤⠤⠤⠖⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠒⠲⠦⢤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠗⠒⠖⠲⠶⠶⠶⠶⠤⠤⠤⣤⣄⣀⡀⠀⠈⠉⠙⠓⠲⠦⠤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣟⠒⠦⠤⢤⣄⣀⣀⣀⣀⣹
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⣽⠁⢹
⠀⠀⠀⠀⠀⠀⣼⣀⣠⡤⠤⠤⠀⢀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢻⠀⠀⠀⠀⠀⠀⡏⠀⢸
⠀⠀⠀⠀⠀⠀⢻⡵⠒⠀⠀⣾⡷⢶⣶⣶⡮⠭⢔⣒⡠⠄⣀⡎⠀⠈⡇⠀⠀⠀⠀⢠⠇⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠨⣽⠿⢶⣾⢥⡀⠀⠀⠉⠓⠦⣕⠦⡀⡇⠀⠀⠀⠀⡜⠀⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠩⣿⡿⣳⣾⢥⡄⠀⠀⠀⠀⠈⠳⡙⡇⠀⠀⠀⠀⣥⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠩⣽⣛⣳⡿⢳⡦⠀⠀⠀⠀⡰⣧⡇⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡀⠀⠾⢯⣽⡿⣣⣿⣢⡀⠀⢻⣿⠇⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣙⢻⣾⣟⣴⡟⣳⣷⡾⠋⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠿⢿⣞⣋⣁⣀⣠⠴⠋





⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢠⣤⡀⠀⣠⣄⠀⠀⠀⢠⣤⡀⢀⣠⣄⠀⠀⠀⠀⣤⣄⠀⢀⣤⡀⠀⠀⠀⣰⣤⣄⣠⣤⡄⠀⠀⠀⢀⡀⠀⠀⢀⣀
⠀⠀⠀⠈⢿⣿⣾⣿⡏⠀⠀⠀⠈⢿⣿⣾⣿⠁⠀⠀⠀⠈⠛⠛⠁⠙⠋⠃⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠉⠙⠁⠈⠋⠉
⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠠⠤⠠⠤⠀⠀⠀⠀⠀⠈⠉⠉⠈⠋⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠚⢿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⣤⣡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣦⣠⣾⣿⡀⠀⠀⢠⣿⣦⣀⣤⣾⡆⠀⠀⠀⠼⢿⠆⠱⣿⠷⠀⠀⠀⢼⣿⣇⣰⣿⡷
⠀⠀⠀⢀⣄⡀⠀⠀⣀⡀⠀⠀⠀⣈⣁⣀⣉⠁⠀⠀⠀⠀⠠⠤⠤⠤⠄⠀⠀⠀⠀⠤⠤⠄⠄⠤⠤⠀⠀⠀⠘⣿⣿⣿⣿⠇
⠀⠀⠀⠘⢿⣿⣦⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢹⣿⣿⣿⡟⠀⠀⠀⢀⣤⣄⣀⣠⣄⠀⠀⠀⠀⣠⣤⡀⣠⣤⡀⠀⠀⠀⣄⠀⠀⠀⢀⡀⠀⠀⠀⣾⣿⢿⣿⢿⣿
⠀⠀⠀⠀⣸⣿⣿⣿⣧⠀⠀⠀⠻⠟⠛⠛⠛⠿⠃⠀⠀⠘⠛⠛⠙⠙⠛⠃⠀⠀⠐⣿⣷⣶⣶⣿⡇⠀⠀⠀⢠⣄⣀⢀⣀⡄
⠀⠀⠀⠀⠉⠻⢿⠟⠉⠀⠀⠀⠀⠓⠒⠒⠒⠂⠀⠀⠀⠘⠒⠒⠒⠐⠒⠂⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠒⠒⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⠄⠀⠀⠀⣴⣶⣶⣶⣶⡀⠀⠀⠀⣠⣀⣀⣀⣠⡀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢰⣶⣦⣶⡆⠀⠀⠀⠀⠈⠉⠛⠉⠀⠀⠀⠀⠀⠉⠻⣿⡿⠋⠀⠀⠀⠀⠉⠻⣿⡿⠋⠁⠀⠀⠀⠈⠁⠀⠀⠈
⠀⠀⠀⠀⣼⣿⣿⣿⣷⡀⠀⠀⠐⠒⠆⠒⠒⠂⠀⠀⠀⠀⠀⣀⣉⣀⠀⠀⠀⠀⠀⠀⣀⣈⣀⡀⠀⠀⠀⣀⣀⡀⣀⣀⠀⡀⡀
⠀⠀⠀⠀⠙⢿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠉⠉⠈⠉⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⠀⠀⠀⠠⠤⣤⣤⣤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⣤⡤⠤
⠀⠀⠀⠀⠀⣒⠒⠂⠂⠀⠀⠀⠀⠙⠻⠿⠟⠁⠀⠀⠀⠀⠀⠈⠿⠁⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠙⠏
⠀⠀⠀⠀⠀⠉⠈⠉⠀⠀⠀⠀⠀⠀⣤⣀⡀⠀⠀⠀⠀⠀⠀⣄⣀⣀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣄⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠼⢄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠧⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⣄⣠⠀⡴⠊⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠐⣀⣀⠀⠀⢸⡇⠀⠀⣀⣀⡄⡠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠤⢽⡴⣒⣋⣹⣏⣙⣒⢦⡯⠤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡾⣛⣿⡿⠋⠉⠉⠙⢿⣿⣛⢷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠋⠉⠀⠀⠀⠀⠀⠀⠈⠙⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⡀⠉⠉⠉⢻⡟⠉⠉⠉⢀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡈⠉⠙⠛⠒⢺⡗⠒⠛⠋⠉⢁⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠦⣬⣉⡙⠛⠓⠒⠚⠓⠒⠚⠛⢋⣉⣥⡴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢬⣍⣙⠛⠛⠒⠒⠛⠛⣋⣩⡥⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⢀⡠⠨⡙⡉⠉⠉⠋⠉⢉⢋⠅⢄⡀⡀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡄
⠀⠀⠀⠀⢰⣖⣴⢄⡀⠀⠈⠓⠶⠚⠁⠀⠀⠀⠀⣤⠤⠤⠤⠤⠤⠤⠤⢤⡀⠀⠀⠀⢀⣿⣿⡟
⠀⠀⠀⠀⣙⣻⣷⣎⡼⠆⠀⢀⡄⢠⣄⣤⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⣿⣿⠃
⠀⠀⠀⠀⢩⣭⠿⣿⡴⢎⠾⣌⣷⣾⡿⢭⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠉⠙⠁
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠷⣿⡿⣯⣙⠓⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⠉⠉⠁⢀⣀⠀⠀⠀⠀⠀⠀⠰⡷⡄
⠀⠀⠀⣀⢶⣘⣷⢰⡀⠀⠀⠘⠳⠆⠉⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠒⠒⠀⠛⠛⠃
⠀⠀⠈⠫⡟⣻⡿⣿⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠙⠁⠉⠀⠀⠀⢺⣷⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡮⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇

⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢀⡀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡇
⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇
⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿
⢀⣾⣿⣿⣄⠀⠀⠀⠀⠀⠀⣴⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣶⣤⡀⠀⠀⣠⣴⣶⣶⣾⠀⠀⠀⠀⢰⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿
⢸⣿⣿⣿⣿⣧⡀⠀⠀⣠⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣆⣠⣤⣄⣰⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣄⣴⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣟⣤⣞⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⡿
⠘⣿⣿⣿⣿⠿⠿⠿⠽⠿⠿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠿⢳⣿⣿⣿⣷⠻⠿⣿⡏⠀⠀⠀⠀⠀⠘⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠍⠭⠙⠿⠛⠓⠶⠶⠶⠴⣷⣶⣿⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣷⣶⣷⡤⠶⠶⠶⠚⠿⠏⠙⠏⠹⣆
⠀⠀⠀⠀⠀⠀⠀⢰⣏⣶⠠⠀⠀⠠⠄⠀⠤⠀⢰⡿⡿⠟⠀⡈⠉⠙⠏⠍⠉⠉⠩⠍⠉⠭⠉⠡⠄⠀⠻⣿⠟⠀⢁⡈⠒⠀⠀⠠⠄⠀⠤⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⣄⣈⢠⡀⠀⣄⠀⢠⠀⢸⠃⠠⠄⠀⠀⡑⠦⠀⠀⣰⠀⠀⡄⠀⣠⠀⢀⡄⠀⣸⡀⢠⡈⠀⣄⠀⢀⠀⣀⣤⠴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣄⠀⢀⠀⢀⡏⠀⡀⠂⠀⠠⣀⠀⠓⣂⠀⢀⡀⠀⠀⣴⠀⠀⢀⡀⠀⢳⡀⠀⡀⠀⣠⡴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢯⣤⠎⠁⠀⠁⠀⠈⠀⠀⠀⠀⠉⠀⠈⠁⠀⠀⠉⠃⢠⠀⠀⠾⠛⠳⣨⡵⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠃⠀⠛⠀⠘⠃⠀⠛⠀⠘⣁⡈⠁⠄⠈⠡⠦⡅⠀⢀⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣶⠀⠰⠀⠐⠆⠀⠲⠈⠁⠀⢀⠀⠀⠀⠺⢆⣰⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠤⠀⣤⡀⠠⠀⠀⠠⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣆⠀⠘⠀⣄⠀⢀⡀⠀⣀⠁⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡂⠀⠀⠀⢀⠀⠀⡀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠈⠀⠀⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢦⣾⣤⣼⣧⡤⠿⠃








⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⡆
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⡇
⠀⠀⠀⠀⠀⠀⠛⣿⣿⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢻⣿⡋
⠀⠀⠀⠀⠀⠀⠈⢹⠁⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⠃⠉
⠀⠀⠀⠀⠀⠀⠀⢸⢀⣄⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠰
⠀⠀⠀⠀⠀⠀⠀⣸⠟⠋⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠶⢿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠈⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⢰⣿⣷⣷⣶⣦⣀⠀⠈⢳⡀⣤⡀⢀⣤⠀⡤⠎⢀⣀⣤⢤⡄⣤⢤⡇
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣻⣿⣷⡦⢻⣿⣿⣿⣿⣿⢷⣶⣿⣣⣼⣿⣿⣿⣳⡇
⠀⠀⠀⠀⠀⠀⠀⢹⠻⣿⣾⣿⣽⣿⣣⣨⡾⣟⣿⣻⢿⣿⣷⣿⣿⡾⣿⣿⣙⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣆⣈⣹⡿⠿⠿⠿⢿⣿⣿⠻⠿⣿⣿⣿⣿⡿⢿⣿⣿⠿⠛⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠋


⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣤⣤⣤⣤⣤⣤⣤⣾⣶⣦⣤⣤⣤⣀⣀⣀⣀⣤⣤⣤⡤
⠀⠀⠀⠀⠀⠀⠀⣼⣿⡵⢪⣑⣏⡰⣿⡼⣾⣿⣽⢏⣻⣇⣼⡿⣽⡍⢻⡍⢯⣟⣾⣛
⠀⠀⠀⠀⠀⠀⠰⣿⣶⢶⣦⣥⢿⣿⢫⣱⣧⡂⠟⠙⡄⠻⣽⢟⣿⠻⣧⡷⣩⣿⣤⣯⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠆⣀⠔⠻⣾⡏⣿⢏⠻⠔⠛⣛⠉⠓⣿⣴⠟⢋⣙⠟⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢾⣹⣗⢻⡾⢻⣤⡥⢼⣴⢋⣼⠟⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣻⣯⣄⣾⣢⣖⣁⣛⣹⡏⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⢀⠱⠀⠀⠀⠀⠀⢠⠃⠃⠀⠀⠀⠄⠀⠒⠀⠀⠀⠀⠄⠒⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⡄
⠀⠀⠸⠀⠃⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠉⠁⠀⠈⠁⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⡜⢣⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠘⡟⠀⠀⠀⠂
⠀⠀⠀⠉⠱⠉⠀⠀⠈⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠺⠧⠄⠀⢀⡀⠀⠠⢤⠶⠶
⠀⠀⠀⣄⡜⠀⠀⠀⠀⢘⣠⠆
⠀⠀⠀⠈⠙⠛⠳⠶⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠒⠆⠠⠤⠤⣠⠤⠤⠄⠒⢢⠀⠀⠀⡀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⡂⠤⡀⠀⠈⠈⠀⠀⡀⠔⡾⠀⠀⢀⢃⠀⠀⠀⠀⠀⠀⠀⢋
⠀⠀⢀⣀⡀⠀⠠⠀⠀⢀⣀⠀⠀⠀⠀⠈⢢⡀⢀⠀⠀⠠⠊⡠⠊⠀⠀⠀⣈⠀⠄⠀⠀⠀⠀⠀⡈⠈⡀
⠀⢜⠁⠀⠀⠈⢧⡾⠁⠀⠀⠉⡢⠀⠀⠀⠀⠙⠢⣄⢠⠥⠊⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠠⠁⠈⢫
⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⣸⣾⡅⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠠⠄⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠉⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠞⠻⠛⠋⠁
⠀⠀⠀⠴⠄⠀⠀⠀⠀⠀⠴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⣀⠀⠀⠀⠀⢐
⠀⢀
⠀⠳⠀⠀⠀⠀⡆⢠⠀⠀⠀⢀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⢀⠄

⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠶⠖⠛⣿⡶⢦⣤⣄⣀⣀⣀⣀⣠⣤⡴⣾⠛⠳⠶⣤⣤⣀⡀
⢀⣠⣤⠶⠶⠛⠋⠉⠁⠀⠀⠀⠀⠈⢷⣄⡀⠀⠉⠉⠉⠉⠁⣠⡾⠋⠀⠀⠀⠀⠀⠉⠉⠛⠳⠶⣤⣄⡀
⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠶⠶⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠙⠦⡴⠶⠶⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠶⠶⠦⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣤⣠⣄⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣴⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠖⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⡶⠲⠶⠶⠶⠲⠖⠋⠀⠀⠀⢰⡏⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠸⣇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣤⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣁⣅⣤⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢠⠖⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢹⡆
⠀⠀⠀⡟⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠂⢈⡇
⠀⠀⠀⢁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢸⠇
⠀⠀⠀⠘⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡏
⠀⠀⠀⠀⠐⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟
⠀⠀⠀⠀⠰⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣇
⠀⠀⠀⠀⠀⣿⣕⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣽⡇
⠀⠀⠀⠀⠀⢷⡟⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢱⣿
⠀⠀⠀⠀⠀⠸⡇⢶⣷⡤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⣄⠠⠾⡟
⠀⠀⠀⠀⠀⠀⢻⡜⠉⠉⠑⠠⢙⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠁⠐
⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠐⠢⡉⢦⡀⠀⠀⠀⠀⠀⠀⢀⠴⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠱⢄⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⢸⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⡈⠆⠀⠂⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡘⣸⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⣠⠀⠀⣤⢠⡄⣀⡱⠷⠃⠀⠶⠀⠦⢠⢀⡄⢀⡄⣀⢀⡀
⠀⠀⠀⠀⠀⠀⡠⠶⠀⠁⠈⠀⠀⢀⡀⢀⠠⠀⠠⠀⠄⠀⠀⠄⠀⠤⠀⡄⠀⡀⣈⢁⡁⠈⡑⣀
⠀⠀⠀⠀⠀⠐⠂⠒⠂⠁⠈⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢠⣄⣄⣤⠲⢄⣀⠐⢒⣂⡐⣶⠖⠦⠀⠖⠲⠀⢘⠓⠈⠘⠉⠁⠈⢀⡴⠖⠃⠼
⠀⠀⠀⠀⠀⠀⠶⢢⠄⡈⣛⠁⠐⠀⠤⠠⠤⠀⠀⣀⠀⠀⠤⠤⠀⠐⠐⠂⢀⣈⠥⠔⠚
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠈⠀⠋⠑⠒⠐⠶⠒⠰⠤⠤⠤⠤⠀⠴⠒⠲⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠐⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠
⠀⢀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⡄
⠀⣼⡁⠀⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠴
⠣⠴⠬⣈⠉⠐⠒⠲⠦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠐⠋⠀⢀⢀⠤⠋
⠀⠐⠀⠀⠈⠁⠒⠠⢀⣄⡈⠀⠀⣀⠀⠀⠀⠀⠂⠀⢀⠀⠀⠁⠀⠀⠀⠀⣤⠦⠐⠈⣀⡀⠔⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣈⠐⠤⣤⠃⠀⠀⣸⣀⡀⢈⡄⠘⠃⠀⣀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⡌⢹⠋⠀⠀⠀⠈⠃⡤⠔⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠂⠉⠁⠁⠀⢠⡞⣾⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⠱⣿⠛⠻⠿⠿⣿⣷⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡬⣿⡀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠉⡲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣻⢤⡀⠅⠀⠀⠀⠀⠀⠀⠀⢣⡘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢿⣷⣶⣶⣤⣤⣤⣀⣀⡀⠙⢾⣙⣷⣆⣀⡀⢀⠀⠀⠀⢀⠀⢂⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣬⣭⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠿⠖⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠊⠉⣼⢾⣿⣿⣿⣿⣷⣦⣀⣀⣀⠤⠤⠀⠠⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠉⠀⠀⠀⠀⠀⢻⠼⣿⠿⠿⠿⠿⠿⠛⠃⠁⠀⠀⠀⠀⠀⠐⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢁⠐⠁⠀⠀⠀⠀⠀⠀⠈⢧⡸⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣝⣻⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠙⠳⢮⣻⢷⣶⣄⣀⣤⣷⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣝⡳⢄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣡⣤⣤⡾⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣾⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠉⠉


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣷⣒⣯⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣗⡦⣀⠀⠀⣀⣤⠶⢚⣛⣿⣽⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡯⠤⠤⢿⣷⣾⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣄⣀⣀⣠⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⢿⣿⡿⠟⠛⢿⣿⣿⡿⠿⠟⠛⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⡿⠿⠟⠻⠿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⠋⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇

⣿⣿⠛⢿⠛⡟⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠉⠻⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠛⠉⠉⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠉⠻⢷⡄⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡟⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠘⣄⠀⠀⠀⠀⠐⢂⣿⣏⣉⡄⠀⠀⢀⣀⣤⣤⣤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠉⠉⠉⠙⠛⠛⠛⠻⠄⠳⠈⠉⠉⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣤⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠇⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣀⠀⠐⢷⠿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⡏⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠏⡐⠁⡜⠃⢠⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠆⣀⠀⠀⢜⡁⠀⠀⣰⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠒⡀⠓⠨⢰⡄⠈⢡⣆⣀⠃⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣛⡠⠛⢆⢠⡤⠀⠈⢣⡀⠺⢯⠌⡀⠶⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠋⠽⠀⠀⠀⣿⠟⢃⡐⢢⠽⠆⡘⠀⣧⡾⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠉⠑⣿⡏⠓⠡⠚⣇⠀⠀⠰⡄⠘⠃⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣤⣒⣒⠒⠫⠄⠻⣶⠤⣛⠿⠾⢠⠺⣉⠀⠄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣀⣂⡔⠉⢻⠙⠋⣼⡷⢄⠐⠶⠀⠠⠼⠇⢁⡘⠀⠙⡂⠀⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡀⠀⠀⠠⢋⠙⠛⢶⣻⣄⡠⠇⡀⠀⢁⡀⠄⠠⡓⢈⣉⡼⣻⠊⠀⢈⠙⡇
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠛⠷⣀⠀⢯⡆⣴⡞⠀⢹⠀⠀⠀⣠⠼⣧⣌⣱⠋⠈⣰⡟⠋⠉⠃⠸⣦⡇
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢰⠃⠀⢬⡄⡠⢄⣉⠤⡑⠚⢀⣁⢀⣼⠋⢱⡂⠄⣻⢆⣀⣰⠆⠶⠈⣧
⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⡀⠀⠤⣴⠁⢻⡇⠐⠈⠁⠀⠀⡤⢚⠁⣈⠁⠒⣈⠇⠀⠙⠲⠾⠅⠐⠀⠀⢹⡆
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠶⢦⣬⣤⣁⣁⣀⣀⡀⠀⠚⢠⠟⠀⠀⠈⠀⠀⠀⠀⣙⣶⣀⣤⣤⣴⠾⣻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡸⢂⣷⠟⢷⡼⢋⡭⠛⢩⣏⣽⢿⣟⠟⡳⠟⣛⠿⣛⣻⣿⣍⡻⢋⣪⠙⣿⠷⣯⣹⠁
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠟⠁⠀⠀⠙⠶⣿⣴⡾⠋⠁⠀⠙⢷⣍⡐⠗⣨⡾⠋⠀⠉⠳⢦⣤⣾⠃⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠀⠀⠀⠀⠀⠀⠈
⠀⠘
⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡴⣀⣤⣤⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⡀⠀⡄⠑⣀⡁⠶⡉⣣⡜⢧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠸⣟⡄⡸⣾⠀⠀⠀⠐⠠⠀⡐⠂⡂⢢⡀⠀⠀⢀⠰⣄⠩⢤⠘⢣⣄⠹⣆⡙⣥⠚⡾⠋⠀⠀⡄
⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⠚⠛⠘⠂⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⡈⢤⡈⢤⡀⠻⡤⠑⢢⡈⢵⠆⠓⠀⠈⠈⠀⠸⢡
⠀⠀⣤⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠎⠱⠦⠉⠠⠚⠓⠂⠉⠀⠀⠀⠀⠀⠀⠉⠀⠖⠃
⠀⠀⠀⠀⠛⠃⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⢠⡤⠶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠟⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠀⣀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⣠⡤⠧⠀⢀⡤⠀⠀⠀⠀⠀⠀⡤⢀⣀⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡔⠂⠀⠛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⣀⡀⠛⠀⣠⡶⠀⠀⠀⠠⠇⠉⠉⠉⠉⠛⠉⠉⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠆⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠁⢀⡤⠖⠀⠀⣀⣠⢠⣤⣤⠶⠶⠴⠁⠀⠄⠀⠀⠀⡄⠀⠀⠀⠀⣀⡀⠰⠁⠀⡀
⠀⠀⠀⠀⠀⢈⠛⠃⠀⠀⠀⠀⢲⣶⣾⡦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠘⠲⠆⠒⠊⠀⠀⠀⠀⠈⠉⠠⠈⠀⠁⠉⡗⠂⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠓⠁⣀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⢀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠄⢤⠀⠀⠧⠎⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠹⠁⠠⠀⠀⡀⢀⡀
⠀⠀⠀⠀⠀⠈⡦⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠰⠀⠘⠀⠀⠃⠀⠅⠀⠐⠀⠀⠀⠀⡶⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣐⢁⠺⠁
⠀⠀⠀⠀⠔⠋⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠘⠀⠈⠁⠁⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⢘⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠂⠀⠀⠈⠀⠐⠀⠀⠀⢄⠀⠀⠀⠀⠀⠰⠀⠀⠀⢠⠤⠊
⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠀⠀⠀⠀⠀⠠⢤⠄⠈⠀⠀⠀⠈⡀
⠀⡀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡰⢆⠴⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠉⠁⠉⠀⠀⠀⠂⠀⠠⠤⠄⠤⠔⠈
⠀⠀⠀⢀⡀⡧⠀⠴⠆⠀⠀⠀⠀⠀⠀⢳⣀⠀⠀⠀⠀⠀⢂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠙⠓⡼⠆⠀⣀⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⠐⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠒⠈⠁
⠀⠀⠀⠐⠒⢤⡄⠀⠈⠁⠀⠀⡀⠀⠛⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠈
⠀⠀⠀⢀⡀⠀⠀⠟⠀⠀⠴⠀⢁⢄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣚⠁
⠀⠀⠀⠀⠁⠀⠷⠀⢰⡀⠀⠀⠀⠨⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠐⠆⠀⠀⠌⠀⠀⠀⠀⠀⡰⡀⠀⠀⠀⠀⠀⠀⠀⠒⠹⠀⠀⠀⠀⠀⡶⢠⡀⢒⠝⣇
⠀⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠠⠈⠃⠀⠀⠀⣀⠀⠀⠀⠈⠇⡈⠕⠉⠀⠉⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⢁⠀⠃⠠⠄⣄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠉⠉⢧⣀⣀⠜⠈⣨⡑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣿⣿⣷⣀⠀⣀⣼⣿⢛⢳⣄
⠀⠀⠀⠀⠀⠀⡠⠞⠁⠸⠗⠀⣶⠄⢸⡁⢴⡆⠉⢁⣄⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣤⣾⣏⣈⣿⠃⢿⣁⣹⣷⡟⡻⣿⣦⡀
⠀⠀⠀⠀⠀⢎⠀⠰⠆⣀⣤⠀⠀⠀⢹⠃⠀⠀⢀⣬⡉⠀⠺⢏⡗⠀⠀⠀⠀⠀⠐⢿⣯⣂⡿⠟⢻⡿⣿⣿⡆⣾⣿⢿⡟⠛⢾⣿⣤⡼⠂
⠀⠀⠀⠀⠀⠀⠳⠔⠊⠁⢸⠘⠟⠀⢾⠆⠐⠛⢸⡀⠈⠑⠦⠊⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢸⣄⣼⣿⣀⣽⣧⣤⡇⠀⠀⠈⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⣄⠀⢀⣤⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⢿⣿⡟⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠈⠁⢀⠀⠁⢠⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢿⣶⣿⣿⣿⣾⠟⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠛⠃⢀⠏⢳⠀⠈⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣤⣿⡟⠀⢹⣿⣶⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⠗⡸⠀⠈⡖⠿⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡉⣻⠁⠀⠀⢏⣈⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣠⡄⢠⠃⠀⠀⢸⡀⢔⡆⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⣿⡏⠀⠀⠀⠸⣿⠛⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢬⣀⡞⠀⠀⠀⠀⢇⣠⡤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠷⢵⡿⠀⠀⠀⠀⠀⢻⣷⠿⠇


⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⡻⠟⠻⢿⣿⣿⣿⣿⡿⠿⣿⠿⣿⣿⣿⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠿⠟⠻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡁⡐⢲⠐⢂⣈⣿⣿⣿⣏⣤⠄⠀⢠⣌⣿⣿⠀⠀⠚⢒⡇⡚⠙⠀⠀⢸⣯⣀⡄⠀⠀⣤⣈⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠓⠃⠘⣿⠿⣿⣿⣿⣿⠀⣄⠘⣿⣿⣿⠀⠀⠀⠘⠚⢆⠀⠀⠀⢸⡿⢿⠃⢠⠀⢸⣿⣿
⣿⣿⣿⡿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣀⣰⣇⢁⣼⣼⣼⣿⣿⣧⣸⣿⣄⣿⣿⣿⠀⠀⠀⠛⠀⠘⠀⠀⠀⢸⣤⣻⣀⣸⣇⣈⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣦⣄
⠀⠀⠀⠀⠀⠀⠸⣄⣀⡀⠔⠚⠉⠉⢀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠛⠿⠟⢲⣦⣤⣤⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠉⠉⠉⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⣼⢃⠿⣶⣤⣄⢉⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣶⡬⣡⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠘⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣂⣠⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠙⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⢀⣄⡀
⠀⠀⠀⠃⠀⠀⢤⣀⠞⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠈⢠⡄⠁⠀⠀⠁
⠀⠀⠀⢶⣨⣀⡰⠀⠩⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠷⠀⠀⠃⠃⠒⠰⠾⠎
⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⢀⢤⡄⢤⣤⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⡠⠴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣟⠀⠀⠀⠀⠀⢈⢥⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⡄⠀⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀

⣿⡯⣿⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⡀⠉⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⣤⡼⠄
⠀⠀⠀⡰⠀⠀⠀⠀⠈⠉⠓⠲⠦⢤⣤⣄⣄⣄⣀⡀⡀⠀⡀⠀⠀⣀⣀⣀⣀⣤⣤⠤⠶⠞⠛⠉⠉⠀⠀⠘⡀
⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠
⠀⠀⠈⠳⢦⠉⠙⠛⠒⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠖⢛⣿⠉⣹⠞⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠙⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⢀⡿⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⢀⣠⠴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⠌⢷⣄⣀⣀⣀⣀⣀⣰⠏⠀⠠⠔⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢶⠒⠒⠒⠊⠉⠉⠉⠉⠙⠉⠙⠒⠒⠒⠒⠒⢤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⣹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣲⣤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⡾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠻⣿⣤⣏⡒⢄⠀⠀⠀⠀⠀⣴⣨⣆⢨⢽⣯⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⠛⣿⠻⡸⣽⡿⣷⠀⢀⣴⣿⣿⠛⡸⣼⢻⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣿⣿⠏⣵⣼⣿⡿⠟⢡⣬⣷⣷⠇⣹⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠌⠵⠇⠈⠁⠀⠀⠈⠙⠿⣽⡤⠯⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢋⢰⣲⡖⠖⣰⠄⢀⠲⣶⠖⠐⣖⣶⠒⢊⡇⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣟⢿⣄⢈⠛⢶⣽⣆⣢⢭⢻⠋⣇⠀⡙⠓⣮⣷⡺⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣟⢤⡈⣍⣩⡞⣯⣟⡷⣇⣠⢔⢩⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢻⣤⠵⣬⢿⣽⣷⣾⡽⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⡖⠋⡺⠛⣽⡗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠙⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠀⠀⠀⠠⠀⠀⣠⣤⣄⡀⢠⠔⠆⠀⣀⣀⠰⣇⠆⢰⠀⣦⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⢰⣛⣯⣍⢹⣿⠷⠤⠞⠿⠷⠥⠤⠇⠀⠘⠶⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⠀⠈⠀⠀⠀⣰⠛⠂⢀⣄⣜⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⠎⠛⠛⠛⠙⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣀⣀⠀⠀⠀⢀⡀⡀⠀⣀⣀⡀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⣈⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⡄⠀⠀⠀⣧⣉⣭⣿⣟⣿⣉⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣉⠉⣉⡉⣙⣻⠀⠀⡁⠀⠀⠀⠀⣁⠀⠀⠀⢰⣶⣶⣷⣶⣶⡆⠀⠀⠀⠀⠀⠀⠈⠀⢰⠶⠓⠀⢰⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⡖⣴⠾⣾⠏⣽⠐⣮⡀⣞⠚⠛⣧⣟⣶⡄⠀⠎⠉⠉⠉⠉⠉⠉⡆⠀⠀⠀⠀⠀⢀⣤⣼⣿⣿⣇⣴⣖⠄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠀⠚⣿⣇⣼⣄⠁⠈⠅⢈⡀⣁⠀⢄⡀⢀⣤⣤⣤⣤⣤⣤⣴⣧⣿⠷⣶⠀⠀⠀⣤⣀⣼⣯⣈⣉⣿⣤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣿⣿⣿⡘⣿⣿⣿⣿⣿⣾⣿⣿⣤⣼⣿⣿⣿⣽⣽⣿⣿⣷⣤⣤⣄⣀⣠⣾⣥⣤⣿⣿⣭⣽⣿⠟
⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠁⠀⠐⠀⠂⠀⠀⠀⠀⠀⡄⠀⢂⡀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠈⠛⠀⢈⠉⠁⠉⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠆⠀⠀⠀⠀⠀⠀⡇⠀⣀⣠⠀⠑⠀⠂⠀⠰⠂⠀⡀⣉⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠈⠀⠈⠉⠉⠁⠈⠀⠉⠉⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠠⠤⠤⠀⠀⠀⠠⠀⠀⠀⠀⠤⠀⠠⠤⠀⠀⢠⣄⣀⣀⣀⠀⠀⠀⣀⡀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠿⠛⠛⠛⢿⣭⠉⠉⠉⠉⠉⠉⠉⠉⠉
⣿⣿⣿⣿⣏⡍⣥⣤⣐⣐⠶⠂⠈⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⠛⠛
⣿⣿⣿⣿⣿⢹⡏⠉⠉⠉
⣿⣿⣿⣿⣿⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠈⠣⣀
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂
⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣴⣾⣿⣿⣷⡄
⣿⣿⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣶⣿⣿⣿⣿⣿⢿⣿⣿⣿⡟⣿⣿⣿⣿⢿⣹⣆
⣿⣿⣿⣿⡏⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⣽⣿⣿⣾⣿⣿⡿⢿⢿⣿⢿⢍⢎⣶⠟
⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⡿⣿⣿⣿⣟⣏⣍⣻⣿⣿⣷⣦⡶⡿⡍⣁⣶⡿⠋
⣿⣿⣿⣿⡿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠋⠳⣷⣼⣤⣴⣛⡙⢍⠉⠩⣻⣿⣗⣢⣽⣾⡿⠋
⢿⣿⡿⡿⠇⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⡿⠻⠛⠋⠁
⣿⣿⣏⣥⣤⠀⡇
⣿⣿⣯⡟⠉⠀⢁
⣿⣯⣤⣤⠀⠀⢸
⣶⣶⡄⠀⠀⠀⠀⡀
⠒⠂⠀⠀⠀⠀⠀⠁
⠐⠀⣀⡀
⠖⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⡶⠶⠶⠖⠶⠶⠶⠦⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠁⠢⡈⠒⠤⠀⣀⣀⠀⠠⠔⢁⠜⠉⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡇⠀⠀⠀⠀⠀⠁⠒⠀⠀⠀⠀⠒⠂⠁⠀⠀⠀⠀⠈⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣀⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢃⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠑⠀⠢⣀⣀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡜⡐⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⢢⠡⡀⠀⢸⠀⠀⠀⡠⠒⠂⠀⠀⢀⡀⠀⣀⠀⠀⠀⠓⠂⡄⠀⠀⡇⠀⢀⠎⠔⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡑⣈⡶⢾⠀⠀⠀⡀⠀⠀⣀⠀⠀⠀⠂⠀⠀⠀⠀⢀⡀⠄⠀⠀⣷⢶⡁⢊⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⣿⠀⠀⠀⠈⠀⠉⠉⠢⠀⠀⠔⠓⠠⠤⠐⠁⠀⠀⠀⠀⣿⠈⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠐⢲⠀⠀⢤⠤⠤⢤⠀⠀⢀⡤⠤⠄⠴⠒⠀⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠀⡀⣈⠀⠀⠸⠀⠀⠨⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠋⠈⠈⡏⠀⠀⠘⠂⠀⠀⡗⠀⠀⠘⠃⠁⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠢⠄⢠⡄⠀⢀⡁⠀⠀⢀⠀⠀⠀⢠⠀⠀⠀⣂⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢸⠀⠀⠀⣼⣇⠀⠀⠘⡁⠀⠀⠉⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠒⠂⠶⠤⠤⡤⠀⠀⢰⠇⠘⣧⣀⣀⣃⠀⢀⣸⣀⡀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠇⠀⠀⠃⠀⠀⣾⠀⠀⢹⡄⠀⠸⠀⠀⠀⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠐⠒⢴⠠⠤⢼⠤⠤⢴⡇⠀⠀⠸⡧⠀⠀⡆⠀⠤⡧⠀⠐⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⡈⠀⠀⡀⠀⠀⣸⠁⠀⠀⠀⣷⠀⠀⠃⠀⠀⢠⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠐⡗⠒⠒⡗⠒⠒⡿⠀⠀⠀⠀⢻⠆⠀⢰⠀⠒⠚⠒⠒⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢸⡇⠀⠈⠀⠀⠀⡆⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠈⠉⠸⠀⠐⢺⠂⠂⢾⠁⠀⠀⠀⠀⠈⡷⠐⠲⡆⠒⠂⠓⠈⠁⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⡀⠀⠀⣈⠀⢀⡿⠀⠀⠀⠀⠀⠀⢿⠀⠀⠁⠀⠀⢸⠀⣀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠤⣤⣯⣄⣀⣭⣠⣴⠇⠀⠀⠀⠀⠀⠀⢸⣁⣀⣛⣈⣁⣈⣀⣤⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉

⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗
⠀⠀⠀⢰⠛⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠛⡆⠀⠀⠀⠀⡟⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⢳
⠀⠀⠀⣜⣀⣄⣀⣉⠢⡀⠀⠀⠀⠀⠀⠀⣠⠔⣉⣀⣀⣀⣣⠀⠀⠀⢰⣃⣠⣄⣈⡓⢤⡀⠀⠀⠀⠀⠀⢀⡴⢊⣁⣠⣄⣸⡄
⠀⠀⢀⠿⠟⠛⠿⠿⣷⣮⣢⡀⠀⠀⢀⣔⣵⣿⠿⠟⠛⠻⢿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⣵⣄⠀⠀⠀⣰⣫⣾⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⡄⣠⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣠⣿⣫⣟⣿⣄⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⢿⣶⣤⣤⣤⣴⣾⡿⠿⠿⢿⠿⢿⣷⣦⣤⣤⣤⣶⡟⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠈⠃⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠘⠁⠀⠀⠀⠀⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠋

⠀⠀⠀⣒⠒⣶⣶⣶⣤⣤⣶⣶⣶⣶⣦⣶⣤⣤⣶⣶⣶⡖⢒⠀⠀⠀⢰⣶⣶⣶⣶⣶⣤⣴⣶⣶⣶⣶⣶⣶⣤⣴⣶⣶⣶⣶⣆
⠀⠀⢀⡉⠉⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠉⠉⢉⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⠻⠿⢿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡿⠿⠿⠃⠀⠀⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⠀⠀⠀⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣿⣿⣄⠀⠀⠀⡴⠻⣟⠳⡄⠀⠀⠀⠐⠆⠈⡋⠂⠄⠀⠀⠀⠤⠂⡊⠐⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣾⣚⡯⣺⣆⠀⣾⣧⣿⠉⣠⣷⠀⠀⠀⢸⣿⣾⣿⣿⣶⣿⢶⣶⣾⣼⣿⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣾⣷⣮⣿⣶⣿⣶⡼⣯⣿⣿⠄⠀⠀⠈⣿⡿⠿⠿⠿⠿⠿⠿⠿⣿⡿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡄⠀⠀⠀⠀⠀⠀⠀⢀⣠⡆⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢾⠉⢿⠲⢦⣤⣀⣤⡤⡶⡏⠁⢱⢤⣀⠀⠀⠀⣾⣦⡙⢄⠀⠀⠀⠔⢡⣾⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣶⣚⣷⣶⣾⣿⣶⣿⣾⣛⣲⠟⠉⠁⠀⠀⠂⢿⣿⣇⠈⢃⡠⠊⣠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠁⠀⠀⢴⣾⠿⠿⠟⠛⠛⠛⠿⠿⠷⣷⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡸⠃⠀⠀⠀⠀⠀⠀⢀⣿⣄⡀⠀⠀⠀⠀⠀⠀⣠⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⢀⡀⠀⠠⠯⠙⠀⠀⠀⠀⠀⠀⢀⡾⠻⡯⢷⣄⠀⠀⠀⣠⠎⢡⠏⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⢏⣴⠀⢺⡰⡃⠀⠀⠀⠀⠀⠀⣸⠇⠀⣹⣬⣽⣧⣤⣴⣅⣀⣾⣴⣈⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣤⣤⣤⣤⣴⣦⣤⣤⣤⣤⣤⡴⠆⠀⠀⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂

⠀⠀⠀⠀⠀⠀⢀⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠐⢦⡀
⠀⠀⠀⠀⠀⠀⠸⣄⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⣀⣤⣾⣶⣻⡞⢁⠀⠀⠀⠀⢠⣶⡷⣦⣴⣷⣄⠀⣿⡄
⠀⠀⠀⠀⠀⢀⣤⠶⠛⣿⢹⣿⣿⣿⢿⡿⢺⢧⡀⠀⣠⣼⡏⣷⣿⣿⣿⣽⢳⣾⣇
⠀⠀⠀⠀⠀⢸⣉⣹⣆⣻⣈⣿⣿⣿⣼⣧⣿⣾⣿⣿⣿⣶⣗⣿⣿⣿⣿⡟⣸⣿⣿⠶⠄
⠀⠀⠀⠀⠀⠈⠯⣍⡈⠻⣍⠉⠛⠿⠿⠿⠟⠛⠁⠀⠙⠿⣿⣿⡿⠿⢿⡶⠿⣿⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⣾⣿⠶⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣲⠶⢶⣶⣶⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡛⣀⣀⡀⡽⠉⢻⡏⢿⣿⡟⠿⠟⣟⠛⢛⡟⠋⠉⠀⢀
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣾⠙⢻⣿⣧⢾⣾⠁⢀⣹⡟⠀⠀⢻⣴⠽⣿⣟⡝⠣⣿⡄
⠀⠀⠀⠀⠀⠀⠼⣿⣿⠟⣶⣼⣟⠸⣾⣏⠶⠒⡌⡇⠀⠀⣽⠟⡡⣻⡯⣾⣶⡟⢿
⠀⠀⠀⠀⠀⠠⡐⠿⠷⣶⣿⣿⣷⣾⣿⣤⣀⠈⣿⣧⡀⢸⣿⡖⣻⣽⣿⡇⣥⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠫⢿⣾⣿⣿⣿⣏⡍⣿⣿⣤⣿⣿⣷⣿⣿⣿⡟⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⢸⠋⠙⠻⣷⢿⡿⣿⣿⡿⣿⠁⠛⢻⡀
⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⢠⡟⠀⠐⠂⠚⣿⣷⣿⠟⠀⢹⠀⠀⢸⡇
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⢸⠀⠀⠸⡇
⠀⠀⠀⣴⠏⠀⠀⠀⠀⢀⣴⡏⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⢠⡏⠀⠀⢠⡇
⠀⠀⠀⠁⠀⠀⠀⠀⠀⡟⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠘⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠉⠛⠛⢿⡆⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠛⠛⠛⠶⠦⣿⠀⠀⠀⠀⠀⠀⣤⣤⣿⣀⠉⠛⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠠⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢰⡟⠀⠀⠉⠛⢶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠘⠀⣾⠁⠀⠀⠀⠀⣼⠇⠀⠀⠂⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠢⡀⠀⠀⣿⠁⠀⠀⠀⠀⢸⡏⠀⢠⠀⠰⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠑⠊⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⣿⠀⠀⡄⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠂⠀⠀⠀⣿⠀⠀⠀⠀⠀⣸⡇⠀⠀⠈⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡇⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⢠⡿⠀⠀⠐⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠅⠀⡀⡀⠀⣷⠀⠀⢀⣾⠃⠀⠐⠈⠁⠀⠀⠀⣿⠁
⠀⠀⠀⠀⣼⠏⣿⠟⠛⠳⠶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠐⠀⠸⡆⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠐⠿⢴⡟⠀⠀⠀⠀⠄⠈⠛⢶⣄⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠻⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⠐⠐⠀⠀⠀⠹⣧⠀⠀⠀⢀⣴⠟⠙⣧⠀⠂⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢠⠀⠈⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⢠⡟⠀⢀⣴⠟⠁⢀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠐⠰⠀⠀⣼⣇⣴⠟⠁⠀⠀⠈⠀⠀⠸⣷⣄⠀⠀⠰⠈⡀⠀⠀⠀⠀⠁⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠁⠀⠀⠿⠋⢁⠀⠀⠀⠀⠀⠀⢀⣤⠿⣝⢷⡀⠀⠈⠀⠠⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢛⣥⣄⠹⣆⠹⣦⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣀⠀⠈⠈⠄⠀⠀⢀⣴⠟⣩⣤⡈⠛⠛⠀⠙⢧⡈⢳⣄⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣡⡶⠟⢻⣄⡀⠀⠀⣠⣾⢋⣥⡀⠈⠛⠁⠀⠀⠀⠀⠈⠻⢦⣙⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⢁⣴⠶⠛⠛⢛⣿⠟⠁⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣶
⠀⠀⠀⠀⠀⠀⠀⢀⡿⢠⡿⠁⠀⢀⣴⣿⠁⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⡇⢀⣴⠟⢹⡇⠀⠀⠌⠀⠀⠀⠄⡀⠄⠀⠀⢀⣤⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢻⡿⠁⠀⢈⣷⡦⠀⠐⠀⠀⠀⠀⠀⣀⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣀⣠⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠶⠶⢦⣤⣤⣤⣤⣤⡶⠶⠶⠶⠟⠛⠛⢻⣦⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⣦⡀⠀⠀⠀⢤⠁⠄⠀⠘⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡿⠶⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠓⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠛⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⣾⣶⣶⣶⣶⣶⣖⣲⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣶⣒⣶⣶⣶⣶⣶⠲⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣿⣟⡿⣿⣿⠿⠿⠛⠛⠻⠟⠛⠛⠛⠛⠻⠿⠻⢿⢟⣿⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠊⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣰⠏⠁⠈⡄⠉⢳⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣿⠀⠀⠀⠀⠀⢰⡇⠀⠀⢐⡀⠀⠀⣤⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡏⠀⠀⢀⣠⣀⡈⢷⡄⠀⠐⠀⠀⣰⠃⣀⣀⣀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡃⢉⣿⠀⠙⠷⠶⠶⠚⣡⣏⡹⠈⠛⣦⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⢸⣙⣓⣿⠀⠀⠀⠀⠀⠐⣯⠢⡅⣢⠜⣸⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣇⢺⡇⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠙⢷⡤⡤⠴⠋⠀⠠⠇⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⣇⡀⢸⣒⣔⣶⣘⣆⡠⡤⠀⠀⠀⠀⣰⣶⣶⣼⡆⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣰⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣀⣀⣀⣒⣻⣿⣿⣻⣶⣒⣦⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠋⠉⠉⠉⠹⠿⣛⢛⡛⠛⢛⣛⡛⣛⣛⣛⣛⣛⠛⠛⢻⠋⠋⠋⠉⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⡄⡇⠀⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣉⣉⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⣉⡉⠉⠉⢁⣀⣀⣀⣈⣉⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠃⠀⠀⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠇
⠀⠀⠀⠀⠐⣶⡀⠀⣹⣦⠀⣴⠁⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡅
⠀⠀⠀⠀⠀⢻⣿⡷⣾⠗⣿⡿⡄⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇
⠀⠀⠀⠀⠀⠸⣿⣷⢸⢹⣿⠃⣇⣀⣀⣀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠀⣇⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠸⣿⣮⣼⣿⠀⠠⠀⠀⡆⢰⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⡀⡆⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢻⣠⣤⣦⣤⣥⡼⠿⠻⠛⠻⢳⣶⣶⣶⣶⣶⣶⠶⠿⠾⠿⠿⢦⣷⣶⣦⣬⡄
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⢻⣯⣤⣤⣤⣤⣤⠜⠛⠛⠛⠛⠻⠛⢤⣤⣤⣤⣤⣤⡿⠛⠛⠛⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠿⠿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⢟⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠰⢦⣿⣶⠾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⢾⣷⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠼⢿⡟⠂⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢾⡟⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠐⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⢀⣧⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⡇⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠏⠉⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣶⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠈⠉⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣄⣀⣀⣀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣛⣿⠿⣿⣷⣦⡀⣀⠀⠻⡄⣶⣦⡀⣴⣿⢀⡴⠋⠀⣠⠄⠔⣆⢹⡀⣷⠒⢿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣿⣴⣿⣟⣻⣽⣴⣷⠆⢻⣿⣿⣿⣿⣯⣿⠻⣿⣅⣮⣱⣤⢏⣽⠷⣿⢉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⢿⣿⣷⣼⣷⣻⣿⠟⣀⣩⣼⡟⢿⡾⣿⢝⢿⣿⣾⢥⡿⣮⡷⣻⣏⢹⣯⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣷⣾⣿⣿⣿⣿⣷⣷⣾⣿⣾⣿⡿⢛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠞⠛⠉⠉⠉⠉⠉⠙⠳⠒⠂⠀⠙⠚⠘⠋⠛⠉⠉⠙⠛⠻⢿⣤⣄⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣴⢦⣀⠐⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⡋⠿⢹⡿⢋⡿⠟⢻⣻⠿⡟⣿⠟⣿⠛⠻⣿⡿⣿⠿⣿⡿⡿⡿⣻⣛⣯⡅
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠛⠶⠁⢲⢤⡧⣞⣩⡷⢋⡟⠿⢷⣛⣤⠿⣇⣴⡯⢹⣿⣅⣩⢷⠊⣷⣯⠿⢦⣥
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣽⣾⢟⡿⢦⡴⠷⣿⡉⣄⢸⣤⡁⢨⠁⠓⡄⠘⢨⠷⣻⣏⠙⣷⣜⣃⣴⣶⣤⣾⣥⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢷⠀⣀⡴⠻⣷⡿⠘⡟⠍⠱⢀⠤⠛⠲⠛⠁⢱⣇⣠⡿⠛⠛⢛⡛⠥⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⣥⠞⣿⡇⠿⣰⣶⣄⠒⢀⣹⡄⡴⠂⣹⣟⠑⡖⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣹⣧⡴⢋⢠⡉⠛⠋⠅⠹⡤⣼⡿⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡽⣷⣶⣼⣦⣦⣧⣴⣤⣥⡿⠀⡇
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⡿
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠿⠿⠿⠁
⠀⠈
⠀⠐
⠀⠘

⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⣤⣀⠀⣀⣀⡀⠀⠀⠀⡆⠀⠀⠀⠀⢠⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢈⣄⡀⠀⢀⣀⡁⠀⠀⠀⠀⠩⣦⠌⡛⢄⣬⡅⠀⠀⠀⡷⠀⠀⠀⠀⠘⡆⠀⠀⠀⢀⠧⣀⠀⠀⣀⠰
⠀⠀⠰⣿⣿⣿⣶⣾⣿⣿⡆⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⢰⣿⣿⣶⣶⣾⣿⣷⠀⠀⠀⠸⠀⠀⢑⣄⠀⣀⡀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣰⣾⣒⣶⣒⣢⡀⠀⠀⠀⠿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠈⠋⠹⠋⠝⠙⠏⠀⠀⠀⢰⣿⣟⣽⣽⣿⣿⣧⠀⠀⠀⠀⠘⢿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣻⣿⠛⠛⠋⠀⠀⢀⣀⢀⣨⣿⣥⢤⣤⠀⠀⠀⠀⠀⠀⠠⢀⡐⠠⢀
⠀⠀⠸⠯⣿⣿⢻⢿⣿⡿⠄⠀⠀⠾⣿⢿⠟⢿⣿⡿⠂⠀⠀⠈⠐⠿⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⡀⠤⠌⠀⢆⡀
⠀⠀⠀⠀⠘⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠋⠀⠀⠋⠀⠀⠀⠀⢀⡀⠀⠈⠿⠃⠀⠀⠀⠀⠀⡄⠀⠄⠁⠀⠛⠸⠄⢃
⠀⠀⠶⠂⠀⠘⠛⠁⠀⠀⠀⠀⠂⠀⠀⡄⠀⠀⣀⠀⠀⢀⠀⠛⠉⠀⠀⠀⠀⠀⠆⠀⠀⠀⠛⠙⠛⠋⠳⠞⠛⠛⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⢀⡄⠀⠐⠄⠀⠀⡄⠀⠀⠀⠀⠀⡄⠀⠀⢨⠀⠀⠀⠀⠀⡆⠐⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠼⠇⢸⢷⡀⠀⠙⠁
⠀⠀⢸⣿⣷⣶⠶⣿⣿⣿⡆⠀⠀⢠⠜⠀⠀⠀⠘⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⢀⠾⠟⠀⠀⠸⠻⣄
⠀⠀⠈⠋⠛⠓⠐⠛⠛⠉⠀⠀⠀⠰⣄⣀⡼⠧⢤⣤⠀⠀⠀⢺⣶⣶⣦⣠⣶⣶⣷⠀⠀⠀⣿⣛⣀⣠⣀⠀⢺⣿⡇
⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠉⠛⠁⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⢀⣔⣒⠒⣒⠒⣶⣶⡄⠀⠀⠀⠂⠀⠀⠀⠁⠃⠀⠀⠀⢀⠒⠐⠒⠒⠒⠚⠂⠀⠀⠀⢠⣶⣶⣖⢲⢶⣲⣶⣦
⠀⠀⠀⠐⠾⣿⣿⣿⡷⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃⠀⠀⠀⠀⠈⠒⠀⠀⠀⠸⠿⣿⠋⠁⠒⢛⡿⠟⠃
⠀⠀⠀⠀⠀⠈⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⣘⣿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⡰⠀⠀⠐⡄⠀⠀⠀⠀⣤⠀⠀⠀⠀⡤⠀⠀⠀⡰⡀⠀⠀⡶⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⡀
⠀⠀⠰⠇⠀⠀⠀⠻⠀⠀⠀⢀⡤⠦⣄⣠⢼⢴⡀⠀⠀⡁⢇⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⢆⠀⠘⠀⠀⠀⠀⠈⣭⣨⢿⣧⣤⡼⠃⠀⠀⠁⠘⣤⠇⠈⠀⠀⠀⠀⠀⣀⠀⣰
⠀⠀⡀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠑⢞⣫⠍⠀⠀⠀⠀⠁⠀⠛⠀⠈⠀⠀⠀⠀⠘⠉⠈⠉⠉⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠤⠀⠀⠠⠀⠀⢰⢄⡀⣸⣇⠀⠀⢢⠀⠠⠂⢰⡄⢐⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠰⠶⠀⡀⠤⠠⠠⠐⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠄⢀⡀⠀⠀⠀⣠⠔⠀⠀⣀⠀⠀⠀⠀⢀
⠀⡧⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠀⡀⠀⠀⠀⠀⡂⠀⠀⠀⣤⠀⠀⠀⠀⣤
⠀⢣⡤⠀⠀⠀⠀⠤⡟⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠀⡏⠦⢀⠀⢠⠿
⠀⠘⢤⣀⣠⣀⣠⠔⡁⠀⠀⠀⡴⠄⠀⠀⡔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⣨⠶⣁⣀
⠀⠈⣂⢠⠙⡏⣰⢀⠁⠀⠀⠀⠄⢠⠀⠀⠃⢸⠀⠀⠀⠐⡀⠀⠀⠀⠀⡠⠀⠀⠀⠃⠈⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⠀⠀⠂⠀⢄⠀⠀⠀⠀⠁⣀⡀⢀⠁⡆
⠀⢰⠳⠤⢀⡠⠴⠒⠂⠀⠀⠁⡀⣀⡤⠤⢀⣀⠜⠀⠀⠸⣤⣬⠏⢻⣅⣼⠃⠀⠀⠸⡀⠀⠀⢀⠰
⠀⠀⠀⠶⠁⠀⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠈⠃⠀⠈
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣠⠀⣀⠀⢀⣀
⠀⠀⠀⠀⠀⡄⠀⠀⠂⠀⠀⠀⡘⠁⢠⠐⢤⡞⢁⠀⠀⠀⢤⠉⠉⠉⠁⠄⠀⠀⠀⢀⡀⠒⠫⢕⣪⠄
⠀⠠⠀⠀⠀⡁⠀⣀⡠⠄⠀⠀⠉⠒⢾⡄⣸⠟⠁⠀⠀⠀⠀⠘⠆⠔⠀⠀⠀⠀⠀⠀⠀⠁⠂
⠀⠀⠀⠈⠁⠈⠁

⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⠀⠒⠊⠀⠀⠀⠀⠀⠀⢿⣷⡄⠀⠀⠀⠂
⣀⡀⠀⠈⠀⣀⡰⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤
⠉⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁
⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢠
⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠟
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣂⡀
⠀⠠⢀⣀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣠⠤⠖⠀⢤⠀⠀⠀⠀⠀⡄⠤⠀⠀⠀⠀⠀⣠⠤
⠀⠀⠀⢀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪
⠄⠄⠂⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄
⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢿⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⡀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠨⡐⠀⠀⠀⠀⠀⢄⢰⢠
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⢄⡋⠠
⠀⠀⠀⠀⠀⠀⣴⣦⡀⠀⠀⠰⠂⢀⣀⠉⣀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠈⠣
⠀⠀⠀⠀⠀⠀⣷⠈⠻⠀⠀⠀⠤⠀⣁⠤⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠴⠀⠀⠱⠀⠀⠹⠆⠀⠀⠀⠀⠀⠘⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠁⠀⠁⠀⠀⠊
⠀⠀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠈⠁⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠙⠳⣤⣤⣤⡤⠖⠃⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡏⢹⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⢀⣴⡄⠀⠀⠈⠛⢯⡉⠀⠀⢉⡽⠛⠁⠀⠀⢠⣦⡀⠀⠀⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⡴⠯⢤⣀⠀⠀⠀⣠⠞⢹⠃⠀⠀⠀⠀⢰⣃⡤⢤⣘⡆⠀⠀⠀⠀⠸⡏⠳⣄⠀⠀⠀⣀⡤⠽⢦
⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠈⠳⣤⡞⠁⠀⢸⢀⡴⣿⠀⠀⠛⠋⠀⠀⠙⠛⠀⢀⣄⠀⠀⡇⠀⠈⢷⣤⠞⠁⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⣀⡴⠋⠀⠀⠀⣾⠋⠀⠿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠳⡤⣷⠀⠀⠀⠙⢦⣀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣿⣀⠀⡴⠒⠛⠁⠀⠀⠀⠀⢠⣴⠒⠁⠀⠀⢿⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⢦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⢀⡶⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠶⠶⠶⠶⠶⠶⠶⢶⡶⠶⠶⠶⠶⠶⠶⠶⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⡾⢷⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⡄⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠉⠉⠉⠙⣿⠀⠀⠀⠀⠀⠀⣗⠋⠉⠉⠉⠉⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⢹⣄⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⣿⣏⢹⣟⠻⣿⢟⠟⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢀⠀⠀⡇⠀⠀⠀⠀⢂⠀⠀⠀⢀⠆⠀⠀⠀⠀⢸⠀⠀⠐⠂⠀⠀⠀⠀⠀⡆⠀⠀⠰⠆
⠀⠀⠀⠀⢀⢿⡄⠀⠀⣠⡅⠀⠀⠀⠀⣀⣇⠀⣸⡇⠀⠀⠀⠀⣿⠀⠀⢀⡆⡆⠀⠀⠀⢀⣿⡀⠀⣸⡄⠀⠀⠀⠀⠠⣅⠀⠀⣩⢆
⠀⠀⠀⠀⡎⠀⠙⣶⠊⠁⢰⠀⠀⠀⠘⠁⠈⠟⠁⠈⠢⠀⠀⢸⢿⣷⢶⣾⣿⣵⠀⠀⠰⠧⢧⢹⡾⡽⠼⠆⠀⠀⠈⠀⠈⠢⠀⢀
⠀⠀⠀⠀⠉⠁⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠈⠉⠈⠈⠉⠀⠈⠀⠀⠀⠈⠂⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣀⢀⣀⡄
⠀⠀⠀⠀⠀⡠⠀⣆⠀⣅⠀⠀⠀⠀⠼⠉⠁⠉⠈⠁⠁⠀⠀⠂⠭⠀⠀⠉⠅⠀⠀⠀⠀⡐⠂⠊⠉⠀⠉⠁⠀⠀⠰⠈⢌⠉⠉⠉⢍⡆
⠀⠀⠀⠀⡞⠀⠐⣩⠋⡀⢣⠀⠀⢠⡉⠀⠂⠀⠃⣀⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣄⣀⡀⣀⣀⣠⡤⠆⠀⠀⠁⠢⣡⢰⠔⠊
⠀⠀⠀⠈⠉⠉⠀⠀⠀⠉⠉⠀⠀⠀⠘⠉⠑⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠈⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡆⠀⢀⡆
⠀⠀⠀⠀⠀⢸⡇⠀⣴⠇⠀⠀⠀⠀⡇⠀⠀⠀⡎⠀⠀⠀⠀⠀⢠⡅⠀⢸⠇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⢄⠀⡠⢄
⠀⠀⠀⠀⣠⠎⢳⡜⠸⡄⠀⠀⠀⡴⠉⠢⢀⠊⠱⡄⠀⠀⠀⡀⠀⠁⡠⠁⠀⠀⠀⠀⠀⡰⢠⠀⠀⡤⠆⠀⠀⠀⠀⡂⢀⡀⠞⠀⠀⠁
⠀⠁⠀⢸⣒⣛⣚⣓⣒⣸⠀⠀⠘⠧⠤⠀⠛⠲⠒⠓⠀⠀⠀⠀⠈⠀⠁⠀⠀⠁⠀⠀⠬⠀⡀⠰⠎⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠤⠤⠴⠆
⠀⠀⠀⠀⠉⠉⠉⠉⠀⡁⠀⠀⠀⠁⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠂⠀⠀⢀⠂
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⡀⠄
⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠈⠉⠀⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠄⠒⠒⠒⠦⢄⡀⠀⠀⢀⡠⠐⠒⠒⠲⢴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡀⠀⢰⡀⠀⠀⠙⣆⠠⠁⠀⠀⠀⡆⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠧⠬⣓⣦⣷⣤⠤⠐⠊⠁⠒⠤⠤⠼⣗⣚⡭⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣙⡒⠶⠶⠦⠤⢤⣤⣤⣤⣤⣤⣤⡴⠶⢛⣩⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣬⣉⠛⠓⠶⠶⠦⠤⢤⣤⡤⠴⠶⠶⠚⠛⣉⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⣄⠀⠀⠀⢀⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋

⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠂⠐⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠁⠀⠀⠀⠀⠀⠀⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠃⠠⡀⠀⠀⢀⠀⠀⠠⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠀⠀⠀⠈⠢⡈⠃⠙⠄⣈⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠉⢁⠀⠈⢀⠓⠂⢀⠄⠒⠒⠀⠒⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠃⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢁⣘⡳⠂⠀⢠⠁⠀⡀⠄⠀⠀⠀⠈⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠁⠘⡄⠀⠀⢀⡴⠖⠤⠜⠓⠺⡄⠀⢀⡆⠀⠀⠘⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⡠⣈⠑⠒⠲⡌⠑⠀⠀⠀⠀⡎⡁⠀⣼⠅⠀⠤⠊⢱⡀⠀⢐⣆⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⡠⠐⠉⠐⠐⠂⢤⡊⠀⠂⣋⠠⠀⠰⡄⣀⠁⠠⠤⠀⢱⣀⠇⠀⠀⠀⠀⠀⢫⡀⠀⠀⠓⠈⣀⠀⠀⠀⠀⠑⣄⣴⣌⡐⢆
⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⠉⢉⣢⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠣⡄⠀⠀⠀⠈⠆⠀⠀⠀⠔⠁⠙⢁⠇⠈⡂
⠀⠀⠀⠀⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⡣⢀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⢒⠒⠢⣼⠀⠀⢈⠀⠀⠀⡖⠪⠘⢁
⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠉⠐⠂⠀⠉⠋⠀⠀⠑⠠⡋⠀⠀⠀⠀⠀⠀⠀⠀⡠⠇⢀⠃⠀⢀⣼⣀⡔⠀⢢⠀⠀⠐⡀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢀⡀⠄⠀⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠀⠤⡤⠀⠀⠐⠀⢰⠆⠀⠀⠘⠿⠋⠀⠀⠀⠆⠀⠀⠓⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⡡⠐⠀⠀⠀⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠠⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⡀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⡀⠀⠀⠀⠀⠀⣰⠠⠊⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⠄⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠈⠉⠉⠑⠂⠠⠂⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⢀⠄⠠⠂⢂⡀
⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠈⠈⠂⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠂⠘
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢵⠀⠆
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠰
⠀⠀⠀⠰⠃⠒⠒⠒⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠉⠡⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠀⠤⠀⠰⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠚⠳⠒⠒⠒⠒⠛⠒⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⣠⡇⠀⠀⠈⢋⠀⡀⡀⠜⠃⠀⠀⠸⣧⡀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⡴⠁⡇⠀⠀⠀⢀⠀⢈⠀⠀⠀⠀⠀⠀⡇⠱⡀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⢀⡜⠁⢸⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢹⠀⢱⡀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⡞⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢳⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⡼⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠈⣇⠀⠄⠀⣡⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠁⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠘⠖⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠐⠂⡞⡆⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢸⠁⡇⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠒⠀⠀⢺⠀⣷⠀⠒⠂⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠂⠀⠀⠀⠀⡾⠀⢸⠂⠀⠀⠐⠂⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢰⠇⠀⠸⡆⠒⠒⠒⠂⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠢⠤⢀⠀⣠⡞⠀⠀⠀⢳⡄⠀⠀⠠⠄⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠚⠁⠀⠀⠀⠀⠓⠶⠶⠖⠚⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡿⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⣷
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⢀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢨⡷⢶⣑⣄⣠⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣤⣂⣴⣹⡶⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠸⡽⣯⣿⣯⣿⣆⣜⣅⡷⡀⠀⠀⠀⠀⡠⣏⣝⣄⣾⣯⣿⣯⣿⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣽⣿⣿⣿⣼⣿⣿⣼⣄⣀⣀⣼⣭⣿⣿⣼⣿⣻⣿⣽⣧⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣯⣻⣿⣿⣿⣿⣿⣿⠏⣿⡏⢻⣿⣿⣿⣿⣿⣿⣋⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣻⣿⣿⣿⣿⡿⠷⠶⣿⣷⡶⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣄⣀⣄⣀⣀⣀⣄⣄⣠⣤⣤⣤⣤⣤⣴⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠫⡋⣿⡽⣿⣝⠃⢠⡇⢘⠿⢼⡿⢟⠀⢱⠄⢖⣼⣿⣽⡇⡥⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠤⠢⢦⡛⣓⡯⢴⣄⡗⠀⡴⠈⠰⣆⠁⣧⣰⠆⣗⡝⡳⠶⢒⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠳⣋⣕⣻⣹⢅⡐⠒⢳⠀⠐⢆⠸⣭⣛⣬⢹⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⢈⢯⣀⡷⢋⠈⠡⢗⢦⣠⠿⡁⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⢧⠷⠟⠇⢸⠻⠺⡼⠚⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢁⡯⣸⣞⢽⡈⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠷⠯⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠁⠀⠀⠈⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢀⡀⠔⡄⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡤⢒⡊⠀⠀⢐⡊⠢⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠶⠀⠀⠰⠀⠀⠀⠟⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠷⣀⠐⠂⡠⠮⣀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣤⠁⠀⠙⡌⢡⠋⠀⠈⣤⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠐⠸⠇⠂⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⢀⣾⠃⡠⠀⠀⠰⠄⠀⠰⢄⠘⣷⡀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⡀⠀⠀⢀⣞⣸⣌⠀⠀⠀⠀⠀⠀⠀⢀⣇⣇⣳⡀⠀⠀⢀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠇⢄⠈⣢⠔⠉⠁⠀⠀⠈⠑⠂⠐⠀⠐⠈⠁⠀⠀⠈⠉⠢⣄⠀⡀⠸⢆
⠀⠀⠀⠀⠀⠀⠀⣸⠁⠄⡀⡙⠐⠢⠤⠤⠤⠤⠤⠄⠄⡀⡀⠄⠤⠤⠤⠤⠤⠤⠴⠂⢋⢀⠠⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠹⣜⠀⠳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⡄⠄⠀⢄⠀⠀⠀⠀⠈⠞⣀⣣⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠉⠒⠤⡀⠀⢀⣨⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁


⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣦⡀⠀⠉⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠚⠻⣿⣿⣤⣿⣥⣿⣤⠀⠀⢀⣴⣶⣀⠀⢀⣰⣶⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⠀⠀⠀⢀⣤⡄⠀⠈⡻⡷⠲⣾⣿⣿⣿⠈⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⣤⣾⣿⣿⣿⣦⡟⣿⡇⠀⣿⣿⡿⢧⠀⣿⢩⣿⠀⠹⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠛⠋⢻⠓⢫⣿⣷⣶⣿⣿⣄⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣟⣀⢻⣟⢹⣿⣿⣿⣿⣶⣾⣷⣿⣿⣤⣰⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⢿⣹⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⡇⣽⣿⣿⣿⣿⣿⡅⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⢾⣷⡿⢹⣿⣿⣿⠼⠿⠀⠀⠀⣭⣉⣛⡿⣿⣿⠿⣯⠁
⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢰⢿⣿⣿⣿⣿⣿⡇⢹⣷⣀⠀⠀⠀⣿⣛⣿⣇⣟⣿⣤⣿⡇
⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⠶⣿⣏⣻⣿⣿⡿⡿⠿⣿⣿⣿⡀⢸⢿⣿⣾⣟⣹⣟⣟⣿⣧
⠀⠀⠀⠀⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣅⡴⣿⣟⠋⣿⣿⣠⣷⠀⣿⣛⣦⣠⡿⢅⣹⣿⣿⣿⣿⢹⣿⡷⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠙⠛⠉⠼⢾⠿⣿⣟⣿⡀⢸⢿⠿⢩⣿⣖⣋⣼⣿⣿⣿⣇⣹⣤⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⢿⡿⠿⠿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣖⠒⠲⠖⡒⣿⡟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⣾⣿⣧⡈⢿⡏⢁⣿⣿⣅⣽⣻⣾⣿⠿⣿⠾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⣇⣿⣿⣿⣿⣧⣼⡿⣟⢿⣿⣿⣛⣿⣿⣿⡿⢿⣀⢛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⡁⣸⣟⣟⢻⣿⣯⣶⣾⢟⣾⣿⣿⡭⠻⣯⣩⣿⡿⢧⣼⣻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢻⠍⠹⡟⣿⣯⡥⣤⣤⣾⣏⣸⣿⣵⡿⣷⣾⠿⣿⣩⣿⠿⠿⠏⠉⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⣶⣶⢿⣿⣽⣿⣿⢛⣻⡟⠻⣿⣿⢿⡶⠿⠞⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣩⣤⣾⡛⠻⠏⠀⠱⠚⠋⠁⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡸⡇⣠⠞⠁⠀⣰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⣀⠀⠀⠀⠙⣿⠃⠀⢀⢾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠓⠦⣄⢹⡄⣰⠋⠀⠉⠓⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠈⢷⣧⡏⠀⠀⠀⠀⣠⢞⣣⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⢟⣲⣤⡀⠀⠀⠹⡇⠀⠀⢀⢞⣵⡿⣿⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⢻⣿⣿⣦⣄⡀⣷⠤⣴⣿⣿⣿⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠒⠛⢉⡽⣿⣿⣿⣶⣿⡷⣋⡴⠻⡟⢮⣽⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠀⠑⠲⠾⠟⢒⣫⣥⣶⠿⣿⠛⠛⠛⠛⠛⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢠⣴⡾⠟⠋⠁⠀⠀⢹⡀⣀⣠⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡾⠿⠛⠛⢛⣿⢿⡿⣛⣭⣥⣀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠚⠉⠉⠉⠉⡏⠁⠀⠀⠈⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠶⠦⣤⣤⣤⣤⣧⣤⡤⠶⠛⢉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⡉⠻⢷⣶⣤⣀⠀⢈⡇⠀⣀⣤⣶⠿⠋⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣦⣬⣝⣛⠿⢿⣿⣿⣟⣫⣵⣶⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠋⠁⢰⠇⠀⠀⠀⠀⢉⣿⡋⠉⠀⠀⠀⣿⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣷⣶⣾⣶⡶⢶⠶⠶⠿⠿⠿⠶⠶⠤⠤⣽⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠈⠛⣿⣾⣷⣿⣷⣤⣺⣟⠢⣴⣶⣶⡿⢿⠛⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡊⢲⢄⠀⠀⠀⠀⢸⡇⠙⢻⣿⣿⡿⣷⣾⣿⡿⠟⠉⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢨⠳⣀⠓⠀⣀⣀⣠⣼⣧⣄⣀⣙⢿⣿⣿⣟⣩⡤⠶⠶⠶⠿⠶⠶⡆
⠀⠀⠀⠀⠀⠀⠸⠧⢦⡈⠛⠛⠉⠁⠀⠀⣀⣤⣬⣭⠿⡗⡿⠿⠤⢤⣤⣤⣀⡀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠠⣀⡟⣡⡆⠀⢀⣠⡾⠛⢉⣀⣀⣀⣀⡀⢠⣤⡶⠶⠶⠶⣯⣽⣿⣶⡆⢠⠅
⠀⠀⠀⠀⠀⠀⠈⠃⢹⠈⠀⠰⣿⠷⠶⠛⠛⠉⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⡐⢢⠀⠀⠀⠀⠀⠀⢠⠒⢆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠂⡀⠀⠀⠀⠀⣠⠊⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡧⠀⠀⠀⠀⠀⢸⡁⠸
⠀⠀⠀⠀⢠⡧⠈⠃⠀⠀⠀⠀⠀⡞⠀⣼⡄⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠑⣄⠀⢠⠞⠁⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡏⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠈⡅⠀⢀⠀⠀⠀⠀⠀⠂⠀⠛⠀⠀⠀⠀⠀⠀⠀⣠⢄⡀⠀⠀⠈⡷⢅⠀⢀⣠⠴⣦⡀⠀⠀⠀⠀⠀⠀⡜⠀⣼⡇⠀⠀⠀⠀⠀⢠⢠
⠀⠀⠀⠀⠀⣟⣓⠾⡀⠀⠀⠀⢰⣠⢴⣒⠀⠀⠀⠀⠀⠀⣜⣭⣤⣬⣑⡠⡎⠀⢈⣶⣭⣤⣶⣷⣷⡄⠀⠀⠀⠀⡼⠁⣸⠃⠀⠀⠀⠀⠀⠀⢸⠈⢣
⠀⠀⠀⣠⣾⣿⣿⣿⣿⣆⢀⣴⣿⣾⣿⣿⣧⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢰⡧⠞⠀⠒⠦⠀⠀⠀⢀⠄⠚⠁⠂⠦⡀
⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠟⠁⠘⢿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⠀⠂⠰⠂⠀⠠⢀⣤⡡⠄⠂⠀⠒⠀⡇
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣻⣿⠃⠀⠀⠀⠀⠀⡟⠛⠻⡿⠿⣶⠶⠶⡶⠿⢿⠟⠛⠛⠀⠀⠀⠀⠘⢦⣀⠈⠀⠀⢀⣠⠿⢦⣄⣀⣀⣁⣴⡇
⠀⠀⠀⠀⣿⣿⣷⢿⣿⣿⣿⣿⣿⣿⣷⣻⡿⠀⠀⠀⠀⠀⠀⠸⠀⠀⢡⠀⠸⡀⢀⠀⠀⡞⠀⢀⠇⠀⠀⠀⠀⠀⠀⠹⠛⠳⠞⠋⠁⢸⠀⠉⠉⡛⠉⡿
⠀⠀⠀⠀⠻⣿⠿⢿⢻⡛⢻⡛⠛⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⡀⠀⢡⡬⠀⢀⡁⠀⠸⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⢸⠀⡀⠀⡇⢠⠇
⠀⠀⠀⠀⠀⠘⠂⠀⢢⠁⠄⠐⠜⠀⠩⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠧⠤⠤⠤⠤⠼⠃⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠊
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣠⠖⠒⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⢦⠀⠀⠀⠀⠀⠀⡠⠤⠠⠤⠠⠤⠀⠠⠤⠤⠠⢤
⠀⠀⠀⠀⣾⣧⣀⡀⠀⠀⠀⠀⠀⠀⢀⣠⢾⣷⣀⠀⠀⠀⠀⡟⠻⢭⣛⣛⣛⣛⣿⣉⣩⡭⠭⠛⠛⡄⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠰⠁⠄⠀⢇
⠀⠀⠀⠠⣿⣯⡛⣤⣉⢶⣶⣴⣶⣊⡝⣉⢾⣿⠂⠀⠀⠀⠀⠈⠲⢶⣿⣿⣿⣿⣿⣿⣿⣿⣄⡤⠞⠁⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⢢
⠀⠀⠀⠈⠈⠳⣌⠙⢿⣿⣿⣿⣷⣿⢊⣹⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢠⡇⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠈⠓⠾⣿⣿⣿⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠅⡤⣀⣀⠀⠘⠀⠀⠀⠀⠀⠀⢀⣐⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⠀⠀⠀⠀⠊

⠀⠀⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡆
⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣇
⠀⢠⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⢀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⣾⠈⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⡆
⠀⣿⠀⠹⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡟⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣿⣿⣿⣧
⠀⢸⡇⠀⠙⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠀⢀⣿⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿
⡆⢸⣿⡀⠀⠈⠻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠃⠀⠀⣼⡏⢰⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿
⣿⡀⢳⡻⣄⠀⠀⠹⣿⣧⠀⣤⣀⣄⡀⢰⣿⡟⠀⠀⣠⡞⡽⠁⣼⠃⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣠⣄⣤⡀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣷⡀⠻⣬⢷⡀⠀⣸⣷⣾⣿⣿⣿⣿⣾⣏⠀⢀⣴⣫⡞⢁⣼⡿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢿⣿⣶⣶⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣷⣶⣿⣿⠃⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠘⣿⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⡟



⠀⡴⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣴⠶⠄⠀⠀⠀⠀⠀⠀⣴⣶⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣶⡄
⢰⠁⣾⠁⠀⢸⣿⠩⣿⠀⠀⣿⠉⣿⠀⠀⣿⠏⠛⡇⠀⠀⣿⡄⢇⠀⠀⠀⠀⠀⢠⡏⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣟⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⢷
⣿⣿⣿⣤⣄⣼⠼⠀⣿⠀⠀⣿⠀⣿⠀⠀⢿⡂⠢⣿⣀⣤⣿⣿⣿⠂⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣖⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣿⣿
⠀⠈⠛⠉⠿⠿⠟⠲⣿⠀⠀⣿⠈⣿⠀⠀⢸⡔⠛⠿⠿⠉⠛⠉⠀⠀⠀⠀⠀⠀⠈⠈⠙⠋⠹⠿⠟⠻⣿⣿⣿⣿⢫⣿⣿⣿⣿⡿⠛⠿⠿⠏⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⣿⠀⣿⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠗⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠅⡬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠐⠒⢤⡂⠀⠃⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠾⠀⠀⠀⡜⢹⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠊⠉⠀⠀⠀⠀⢠⠃⠘⠒⢒⡩⠔⠛⢲⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⣿⣷⣄⠀⢸⠀⠀⠀⠀⠀⠀⠈⣁⠠⣇
⠀⠀⠀⠀⠀⡠⠤⠤⠄⣸⣿⣿⣿⡿⠿⠿⠿⠟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⠴⢼
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡤⠚⠁⠀⠀⠳⣄
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣷⠞⠛⠛⠲⢦⣀⠀⠳⣄
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⢈⢓⠢⣈⠳⣄
⠀⠀⠀⠀⠀⣇⣀⠤⠔⠒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢣⠱⡀⠑⠢⢕⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢸⠀⡁⠀⠀⠀⠈⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠆⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡽⡀⠀⠀⠀⠀⢸⠧⡀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠋⠈⠉⠁⠀⡇⢇⠀⠀⠀⠀⠸⠀⠀⠁⠒⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠸⡀⠀⠀⠀⠀⡇⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠒⠒⠒⠒⠒⢲⠋⠀⠀⢣⠀⠀⠀⠀⠇⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠵⠖⠒⠒⠒⠒⠒⠒⠠⢕⣤⡀⠈⡆⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣆⢸⠀⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢣⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠷⢤⡀⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠤⢄⣙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⣒⣒⣒⣒⣀⣀⣀⣒⣀⡀⠒⠒⠒⢒⣒⣒⣚⣓⣒⣒⣒⣒⣖⡒⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⡉⠉⠉⠛⠛⠋⠉⠉⠙⠋⠉⠉⠉⠉⠉⠉⠉⠉⠋⠉⢹⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠶⠶⠶⠶⣴⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⢠⣿⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⢂⡀⡀⣿⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⢸⠟⠳⠁⠞⠀⣿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠀⢀⠀⡐⠀⠸⠤⠤⠤⠤⠤⠿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢘⣦⣭⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡄⣴⠆⠀⠐⠹⠃⠉⠀⠀⢀⣠⣀⡀⠻⠁⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣀⣀⡡⣽⡆⠀⠀⡆⠀⠀⢀⣴⠎⣹⣿⢰⠉⡆⠀⣆⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠥⠨⠯⠴⠷⠿⣼⡤⠿⠶⠦⣾⣷⠶⠿⣿⡾⠦⠷⠾⠷⠶⠶⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠉⠉⠉⠙⠛⠛⠛⣛⠛⠛⠛⠛⠛⠛⠛⣛⣛⠛⠛⠛⠟⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣀⣀⡀⢀⣈⣉⣉⣉⣁⣉⠉⠉⠉⠀⢀⠀⢀⠀⢠⣤⣼⡄⠀⢀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢹⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠙⣤⡤⠖⠋⠻⠙⠛⠛⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠇⠀⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣻⣷⡀⠀⠘⠆⠀⠀⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⣠⠿⠛⠻⢦⣀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⣶⠀⣿⣿⣿⢿⡿⣿⣿⣿⡿⣿⣻⣉⣀⣼⣦⣀⣤⡾⠃⠀⠀⠀⢀⣬⡉⠁⠂⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣀⣀⣀⡿⠀⣿⣿⣽⣉⣇⣶⣿⣌⣠⣷⠉⣿⣿⣿⡿⠿⢿⣱⡀⠀⠀⣀⣼⣿⣿⡄⠀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣟⣿⣟⣁⡀⠀⠀⠈⠙⠻⣿⣿⡇⣿⣿⣿⠊⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⡤⠿⠷⡾⠓⠒⡶⠶⠶⠶⠒⢶⣿⣿⠿⢿⣿⣿⣿⣶⣶⣶⣶⣿⣷⣿⣿⣿⣴⢿⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠎⠀⠠⠄⠀⠈⠭⠀⠠⠤⠂⠀⢿⣿⣿⣿⣿⣿⣷⣷⣶⣿⣿⣿⣿⣿⣿⣿⡏⢀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠁⢀⣀⡀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠫⠿⠭⠉⢉⣉⡙⠙⢋⡽⢻⣿⢟⣏⠜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⣾⣿⠖⠀⠀⠸⠧
⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠙⡇⠀⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄⠀⠀⠀⣧⣄⡀⠘⠀⠀⠀⠀⠀⢀⡀⡀
⠀⠀⠀⠀⢀⡀⠀⠰⠆⠀⢶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠆⡈⠿⠠⠀⠀⠀⢁⠀⡴⠄⠀⢠⣤⠀⠀⠈⠁⡇
⠀⠀⠀⠀⠘⠃⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣿⡎⠀⠑⠀⠀⠀⠢⠸⣎⠄⠀⠀⠀⠀⠃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠛⠁⢀⡀⡈⠁⠀⠀⠀⡀⠀⢀⣀⠁⢸⣿⣷⡄⠀⠈⢀⣠⣴⠀⣿⡆⠀⠀⢠⡄⠀⠀⢀⡄
⠀⠀⠀⢀⡄⠀⠀⣴⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⠁⣡⣿⠟⣿⣷⣤⣠⣆⢣⢿⣷⣿⣾⣷⠀⠈⠁⢀⡀⠀⠉
⠀⠀⠀⠈⠁⢀⠰⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠈⠻⠟⠀⢸⣿⠟⠃⢁⣍⣿⣿⢿⡏⠁⣀⠀⠀⠛⣁⢠⣄⣤⡆
⠀⠀⠾⠀⠀⠋⠀⠘⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⢁⣴⣖⣦⣽⢻⣿⣿⣇⠈⠋⠀⠃⠀⣷⠀⢸⡇⠁
⠀⠀⠀⠠⠆⡶⠀⠀⠀⠀⠀⠀⢠⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣾⣿⣿⡿⠄⠀⣀⠅⢸⣿⣷⣼⡇
⠀⠀⠿⠀⠀⠆⠀⠐⢦⠀⢀⡠⠖⠛⠀⣇⢀⠀⣀⣀⣀⣀⣀⣀⣿⣿⣿⢿⣿⣿⣿⣷⣾⠀⠋⠆⢸⣝⢻⠦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡟⢺⠀⠀⠀⠈⠉⠙⠋⠁
⠀⠀⣤⣤⣤⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣿⣤⣶⣴⣶⣶⣶⣶⣶⡆
⠀⠀⣿⣿⣿⣿⣿⠑⢄⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⢀⣤⡿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⠀⢸⣿⡿⣧⠀⠀⢀⣴⡾⠋⠉⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⡿⠿⠉⠁⠈⢻⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⠀⡛⣹⣶⣿⣦⣴⣿⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠁⢿⣿⡇
⠀⠀⣿⣿⡿⠋⠉⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⣤⣤⣤⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠁⠀⠀⡀⠀⠀⠈⠉⠇
⠀⠀⣿⣿⠁⣾⢏⡰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣶⡿⠀⠀⠀⠀⠀⠸⣿⡇⣄⠀⣄⠘⣃⣤
⠀⠀⣿⡂⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠉⠉⠉⠉⠻⠻⡿⢟⠁⠀⠀⠀⠀⠀⠀⢻⡧⠘⠟⠀⠂⠁⢀⠀⠀⣠⡀
⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⢥⣸⣷⣶⣶⣶⣶⡶⣿⣿⡇
⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣜⣿⡃⢀
⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢣⠀⠀⡀⠐⠈⢠⣤⠟⠁⠈⠀⠀⠘⠋⠋⠙⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠴⠶⠤⠤⠤⠀⠀⠀⠀⠀⠀⠘⠀⠈⠀⠀⠀⠀⠁⠶⠰⢤⠳⣔
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⡉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣴⣶⣴⣦⣤⣤⣤⣄⣤⣀⣠⣀⣀⣀⣀⠀⡀⠀⡀⠀⡀⠀⠀⢀⠀⢀⠀⣀⠀⣀⣀⣀⣀⣄⣀⣤⣠⣤⣤⣤⣴⣦⣶⣦
⠀⠈⠉⠉⠉⠙⠋⣿⠛⠟⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⠿⠟⢿⢛⣟⠙⠋⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠄⠀⠀⠺⣿⢵⣿⠿⣿⣿⣿⢧⣾⣿⣿⣿⢷⡏⡹⢷⣌⣿⠇⠈⠠⠊⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠈⠀⠄⢿⣞⣻⣵⠖⣽⣟⣬⢿⣽⣶⣵⡎⣹⣿⣘⣹⠿⠀⠐⠀⢀⡼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠠⠀⠘⢿⣻⣿⣖⠚⢹⢿⣨⣿⣽⡿⣾⣿⣿⢿⡟⠂⠀⠀⠀⡰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢢⠠⠋⠄⠙⣿⣿⠛⢪⣤⡙⡟⣿⢯⣿⣿⣿⣿⣿⠁⠰⠉⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⣌⡂⠀⣹⣏⣿⣗⡻⠛⣥⣾⣴⣻⣗⡶⣾⡏⡀⠱⢈⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡈⢁⠀⣽⣿⣿⣿⣧⡄⣾⣿⡿⣿⣷⡏⠀⡀⠀⣼⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠔⠈⣿⣿⣿⣏⣽⣿⣿⣿⣯⡯⠀⡠⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠨⣿⡿⣸⣿⣺⣭⣫⡿⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡅⠀⠽⣿⡿⢘⣿⣿⣿⠷⠄⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠐⣿⠺⡿⣿⣟⣿⠆⢳⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣌⢿⠿⣃⣽⣬⣿⣢⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠆⠉⠽⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⢀⠠⠀⠀⠤⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠈⢀⠀⠀⠀⠀⠀⡄⠠⡄
⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⡐⢤⡄⠈⠈
⠀⠀⠀⠀⠸⣄⡀⡀⣀⠀⡀⠤⠤⠄⠀⢸⣄⡀⢜⣄⢸⣄⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡭⠀⠀⡍⣒⠀⠀⠀⠐⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠂⡁⢀⠶⣤⡍⠄⠀⠀⠀⠸⠰⠀⠀⠀⡀⠄⠤⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢔⠀⠀⡱⠁⠀⠈⢶⣄⠤⣖⠐⠢⢠⠐⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠕⠼⡄⠀⢳⡇⡆⡳⣦⠀⢸⢛⡿⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⠀⠀⠀⠰⢠⡎⠄⢸⡇⠏⠀⢘⡏⠉⠐⢰⡆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⢠⠖⣦⡀⣨⠿⠀⠰⡎⠸⣠⢶⡆⠀⠀⣤⣘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠥⠈⠛⡇⢬⡍⠀⠘⠐⠃⡆⠻⢀⠀⠻⣿⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⣀⢧⣯⠀⠁⠈⠀⢀⠄⠀⠀⡴⠋⡄⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⢠⢄⡄⠈⠇⠀⣷⠁⠚⠀⣁⠸⠀⠠⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠛⠿⠻⡴⡶⣿⣤⣤⣄⣀⣁⢣⣴⡾⠇⠀⠈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣴⠳⠀⢣⠀⠀⣨⢈⠁⠓⠛⢭⡁⠀⠀⢒⠒⠂⡚⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠜⠨⠀⠀⢘⣀⠀⣉⡊⠀⢾⠤⠀⠃⢠⡀⡀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠄⠙⠀⠀⠀⠀⠉⠁⠀⠀⠀⠢⠀⠈⠁⠀⠄⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠆
⠀⠀⠀⠀⠀⠀⠂